Question

(1 point) find the point pp where the line x=1+t,y=2t,z=−3tx=1+t,y=2t,z=−3t intersects the plane x+y−z=1.

Answer 1

sub in values for x,y,z into plane equation.

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

Solve for 't'

6t + 1 = 1
t = 0

Sub back in t=0 into line to find point.
x = 1+0 = 1
y = 2(0) = 0
z = -3(0) = 0

Answer : The point is (1,0,0)