Question

The intersection of a plane and a line is a what?

Answer 1

Example:
Linear Algebra

How would you find the point of intersection of the line

x= -5t+9
y= -t-1
z= t+3

and the plane 2x-3y+4z+7 =0

Intersection occurs when all of the equations are simultaneously true.

Substitute x = 9 - 5t, y = -t - 1, z = t + 3 into the plane equation.

2(9 - 5t) - 3(-t - 1) + 4(t + 3) + 7 = 0 ----> t = 40/3

x = 9 - 5t = 9 - 200/3 = -173/3
y = -t - 1 = -40/3 - 1 = -43/3
z = t + 3 = 40/3 + 3 = 49/3

Line intersects plane at (-173/3, -43/3, 49/3).