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428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:38:48 | cuz cos wouldn't start from origin | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 200,013,547,491,688,450 | a disappointing son | 02/01/2022 17:39:07 | right... | 0 | 1 | 200,013,547,491,688,450 | a disappointing son | 0540 | a disappointing son | false | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 200,013,547,491,688,450 | a disappointing son | 02/01/2022 17:39:13 | so possibly your other answer that is already correct is right lol | 0 | 1 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:39:23 | so I put 1.5 again? | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:39:26 | 1.5 and 1.5? | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 200,013,547,491,688,450 | a disappointing son | 02/01/2022 17:39:31 | no | 0 | 1 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:39:33 | X_X | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:39:34 | eh | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 200,013,547,491,688,450 | a disappointing son | 02/01/2022 17:39:36 | it tells you to select the correct function | 0 | 1 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 200,013,547,491,688,450 | a disappointing son | 02/01/2022 17:39:39 | only one of those is gonna be right lol | 0 | 1 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:39:44 | ohhhhh | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:39:45 | ok ok | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:39:59 | omg lol | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:40:03 | what a tricky sneaky question | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:40:07 | that was bs | 1 | 0 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 200,013,547,491,688,450 | a disappointing son | 02/01/2022 17:40:08 | indeed | 0 | 1 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 200,013,547,491,688,450 | a disappointing son | 02/01/2022 17:40:09 | lol | 0 | 1 | null | null | null | null | null | |||||
428 | help-10 | a5d649ba14904bb792d3111e1df02b26 | 351,013,311,996,887,040 | ♡ nahitspanda ♡ | 02/01/2022 17:48:22 | .close | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 17:56:14 | since H_t must be a vector space, does t=0? | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 17:56:30 | since the 0 vector must be within a vector space | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 17:57:45 | and does that imply that s must remain a constant, since the vector that results from the subtraction of two points in an affine space must be contained within its tangent space? | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:07:56 | H_t isn't a vector space in general | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:08:13 | H_t is an affine space | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:09:42 | ? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:09:51 | Or am I misinterpreting notation | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:10:01 | <x, y, z> is just a normal vector or not | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:10:05 | H_t is the tangent space and H_s is the affine space I think | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:10:09 | and yea it's a normal vector | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:10:20 | I don't understand what tangent space means in this context then | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:10:28 | For us it was just defined as | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:10:30 | Geometrically, isn't H_t flat? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:10:40 | Subtraction of two points in H_s will result in a vector in H_t | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:10:54 | and adding a point in H_s with a vector in H_t will result in a point in H_s | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:10:58 | ohhhhhh ok I get it. | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:11:09 | Then yes the tangent space is a vector space | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:11:25 | In particular | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:11:34 | Think about a general plane in 3D space. | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:11:46 | the equation is
**x**.**n** = **a**.**n** = D | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:12:01 | Do you recognise this? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:12:09 | What does the . represent? | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:12:12 | dot product | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:12:37 | No, not really if I'm being honest I don't think we've introduced the dot product in the class yet | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:12:51 | This is university/college stuff or not? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:12:57 | Yes but it's an intro class | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:13:04 | Did you not see plane equations in high school | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:13:14 | cartesian equations? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:13:15 | Yea | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:13:28 | ax + by + cz = D | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:13:33 | Ok got it yea | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:13:38 | But in vectors, you haven't seen dot product? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:13:49 | Is that the inner product? | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:13:50 | That's kinda odd | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:13:51 | yes | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:13:54 | Ok yes | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:13:58 | ax + by + cz = D | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:07 | (a b c) . (x y z) = D | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:12 | if I write those vectors as columns | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:16 | you can see? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:14:18 | Yes | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:23 | **x**.**n** = **a**.**n** = D | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:26 | So we have this form | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:29 | The (a b c) | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:31 | is **n** | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 382,568,504,936,759,300 | Hungry Kitten | 02/01/2022 18:14:40 | got it | 1 | 0 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:45 | For one sec, lets think if D = 0 | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:14:50 | **x**.**n** = 0 | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:15:01 | This means variable **x** is orthogonal to **n** | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:15:09 | yea | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:15:14 | Your plane is all vectors perpendicular to **n** | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:15:24 | sorry I got off my phone I'm here now | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:15:25 | So if D = 0, it turns out **n** is the normal vector to the plane | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:15:39 | ok | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:15:57 | That make sense so far? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:15:58 | So what does this have to do with affine space and the tangent space exactly? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:16:02 | yea I do get it so far | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:16:08 | Because I think it's v. related | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:16:22 | In this case uhh | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:16:34 | I'm pretty sure you have a plane, do you not? | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:16:42 | yea | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:16:46 | since the z is constant | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:16:47 | Right | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:17:06 | So for a shifted plane | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:17:11 | **x**.**n** = **a**.**n** = D | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:17:18 | You are shifting the plane by vector **a** | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:17:24 | If **n** is a unit normal vector | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:17:34 | And D = **a**.**n** | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:17:55 | So actually, I think H_s will be the shifted plane. H_t will be the unshifted plane | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:18:55 | unknown.png | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:19:27 | So back to this, H_s in general is the plane parallel to the xy-plane, s away from the origin | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:19:40 | Sure | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:20:00 | t is the plane at the origin | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:20:13 | And I think Hs and Ht have to be parallel | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:20:23 | Aren't they already parallel | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:20:27 | yh I guess lol | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:20:30 | since we define H_s and H_t with constant z | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:20:32 | So t = 0 is a must | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:20:37 | and s = any element of R | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:20:43 | Yh | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 321,445,119,171,756,000 | Shuri2060 | 02/01/2022 18:20:46 | thats what I figured | 0 | 1 | null | null | null | null | null | |||||
429 | help-10 | a866d67a4e74491fbd334d04b918d41d | 225,110,750,161,666,050 | Neko | 02/01/2022 18:20:50 | is H_t just displacing it up and down then? | 0 | 1 | null | null | null | null | null |
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