Thread: Find the point at which the line intersects the given plane

Find the point at which the line intersects the given plane.

Line: x = y - 1 = 2z
Plane: 4x - y + 3z = 8

I understand how to use the cross product, dot product, and find intercepts. This problem is in section 13.5 #45 of the James Stewart Calculus book. I understand the idea but need some help in solving the problem. Thanks!

Originally Posted by jdj333

Find the point at which the line intersects the given plane.

Line: x = y - 1 = 2z
Plane: 4x - y + 3z = 8

I understand how to use the cross product, dot product, and find intercepts. This problem is in section 13.5 #45 of the James Stewart Calculus book. I understand the idea but need some help in solving the problem. Thanks!

The equation of the line tells you that x = 2z and y = 2z + 1. Substitute those expressions for x and y into the equation of the plane, and you have a simple equation for z.