[
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 0,
        "timestamp": 1684480825133.0,
        "annotatedSourceSentencesIndices": [
            55,
            57,
            51,
            52,
            55
        ],
        "names": [
            "annotator1",
            "annotator2"
        ],
        "text": "where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!"
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 2,
        "timestamp": 1684480921899.0,
        "annotatedSourceSentencesIndices": [
            51,
            52
        ],
        "names": [
            "annotator1"
        ],
        "text": "08:10 how do you express the plan formed by two lines in general? "
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 3,
        "timestamp": 1684510062486.0,
        "annotatedSourceSentencesIndices": [
            293
        ],
        "names": [
            "annotator1"
        ],
        "text": "why is it the the deviation formula is squared? i know it must be equal to zero."
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 4,
        "timestamp": 1684510080674.0,
        "annotatedSourceSentencesIndices": [
            293
        ],
        "names": [
            "annotator1"
        ],
        "text": "Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please."
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 5,
        "timestamp": 1684510172054.0,
        "annotatedSourceSentencesIndices": [
            198
        ],
        "names": [
            "annotator1"
        ],
        "text": "25:57\nWhy he wrote f(-1,0)?"
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 7,
        "timestamp": 1684510713476.0,
        "annotatedSourceSentencesIndices": [
            51
        ],
        "names": [
            "annotator1"
        ],
        "text": "For z = z0 + a(x-x0) + b(y-y0),\nwouldn't that mean:\n-1(z-z0) + a(x-x0) + b(y-y0) = 0\nso from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?\nI'm missing something about the -1 I'm sure"
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 9,
        "timestamp": 1684510838484.0,
        "annotatedSourceSentencesIndices": [
            284,
            285
        ],
        "names": [
            "annotator1"
        ],
        "text": "34:58 would using perpendicular distance (instead of vertical distance) make better sense? \n"
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 12,
        "timestamp": 1684510931819.0,
        "annotatedSourceSentencesIndices": [
            43
        ],
        "names": [
            "annotator1"
        ],
        "text": "6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is  the above euqation realted to this? Thanks in advance"
    },
    {
        "file_id": "UYe98CcxPbs",
        "query_id": 1,
        "timestamp": 1684191408602.0,
        "annotatedSourceSentencesIndices": [
            0
        ],
        "names": [
            "annotator1"
        ],
        "text": "Would any one please explain what did the professor mean between 13:13 and 13:44?"
    }
]