Find the point(s) of intersection between the line L: →r = [−6,9,−1] + t[−2,3,1], t ∈ R andtheplaneπ:−x+2y+z+4=0.

Answer 1

Parametric equations of the line are:

x = -2t - 6

y = 3t + 9

z = t - 1

So, -(-2t - 6) + 2(3t + 9) + (t - 1) + 4 = 0

9t + 27 = 0

t = -3

Therefore, x = 0, y = 0, and z = -4.

The line and plane intersect at the point (0, 0, -4).