Find the point P

Question

Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -3.

Answer 1

To solve for an intersection, you generally set the two intersecting objects equal. Here, we can use the parametric equations for x, y, z of the line to solve for t where it intersects the plane.

 

x + y - z = 3

(1+t) + (2t) - (-3t) = -3

6t + 1 = -3

t = -4/6 = -2/3

 

x = 1+(-2/3) = 1/3

y = 2(-2/3) = -4/3

z = -3(-2/3) = 2

 

The point of intersection is P = (1/3, -4/3, 2)