The parametric equations for a line L1 are as follows:

Question

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)

Answer 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)