( 717, #37 ) Find the point at which the line x = 1 + 2t, y = -1, z = t, intersects the plane 2x + y - z + 5 = 0.

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.

2( 1 + 2t ) + ( -1 ) - ( t ) + 5 = 0

3t = -6

t = -2

The point where the plane and line intersect can be computed by using t = -2:

x = 1 + 2*( -2 ) = -3, y = -1, z = -2

The point is ( -3, -1, -2 ).

by: nl