( 717, #35 ) Find the point at which the line x = 1 + t, y = 2t, z = 3t, intersects the plane x + y + z = 1

( 717, #35 ) Find the point at which the line x = 1 + t, y = 2t, z = 3t, intersects the plane x + y + z = 1.
Solution:
The value t can be solved for by replacing the values of x, y and z in the planar equation with the linear equations.

( 1 + t ) + ( 2t ) + ( 3t ) = 1
6t = 0
t = 0

The point where the plane and line intersect can be computed by using t = 0:

x = 1 + 0 = 1, y = 2*0 = 0, z = 3*0 = 0
The point is ( 1, 0, 0 ).

by: nl