Algebra

The parametric equations for a line L1 are as follows:
x = −1−2t
y = 4+4t
z = 3−2t

Let L2 be the line parallel to L1 and passing through the point (2, 5, −3). Find the point P on L2 whose x-coordinate is −3.
P = (−3, 0, 0)

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  1. The second equation L2 is given by
    (x,y,z) = (2,5,-3) + t(-2,4,-2)

    we want -3 = 2 -2t
    2t = 5
    t = 5/2

    then (x,y,z) = (2,5,-3) + (5/2)(-2,4,-2)
    = (2,5,-3) + (-5, 10, -5) = (-3, 15, -8)

    the point is (-3, 15, -8)

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