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Math Help - Vectors

  1. #1
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    Vectors

    Find the point of intersection of the line through the points (2, 0, 1) and (-1, 3, 4) and the line through the points (-1, 3, 0) and (4, -2, 5).

    -------------

    So far I did:

    Let the line l₁ has points c = (2, 0, 1) and d = (-1, 3, 4).

    So the vector equation of a straight line is

    r = c + t(d - c)

    d - c = (-3, 3, 3)

    So l₁: r = (2, 0, 1) + t(-3, 3, 3)


    Similarly I found

    l₂: r = (-1, 3, 0) + s(5, -5, 5)

    But it seems not right. When I equate the x & y components & solving simultaneously I found no solution. Actually what to do in this case?
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  2. #2
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    Quote Originally Posted by geton View Post
    Find the point of intersection of the line through the points (2, 0, 1) and (-1, 3, 4) and the line through the points (-1, 3, 0) and (4, -2, 5).

    -------------

    So far I did:

    Let the line l₁ has points c = (2, 0, 1) and d = (-1, 3, 4).

    So the vector equation of a straight line is

    r = c + t(d - c)

    d - c = (-3, 3, 3)

    So l₁: r = (2, 0, 1) + t(-3, 3, 3)


    Similarly I found

    l₂: r = (-1, 3, 0) + s(5, -5, 5)

    But it seems not right. When I equate the x & y components & solving simultaneously I found no solution. Actually what to do in this case?
    That's strange because when I equate the components I get:

    i-component: 2 - 3t = -1 + 5s => 5s + 3t = 3.

    j-component: 3t = 3 - 5s => 3t + 5s = 3.

    These two equations are the same.

    k-component: 1 + 3t = 5s => 5s - 3t = 1 => 3t - 5s = -1.

    There's no trouble here ..... Just solve 5s + 3t = 3 and 3t - 5s = -1 simultaneously for t (or s, or both if you want to check the answer).
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    That's strange because when I equate the components I get:

    i-component: 2 - 3t = -1 + 5s => 5s + 3t = 3.

    j-component: 3t = 3 - 5s => 3t + 5s = 3.

    These two equations are the same.

    k-component: 1 + 3t = 5s => 5s - 3t = 1 => 3t - 5s = -1.

    There's no trouble here ..... Just solve 5s + 3t = 3 and 3t - 5s = -1 simultaneously for t (or s, or both if you want to check the answer).
    Yes there is no problem. I solved it There's silly mistake.

    Thank you.
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