Find the point of intersection of the plane x y 2z 0 and

Find the point of intersection of the plane x + y + 2z = 0 and the line whose parametric form is x = 2 + t y = 1 + 2t z=3 + 1

Solution

x + y + 2z = 0

x = 2+t , y = 1 +2t , z = 3+t

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

==> 9 + 5t = 0

==> 5t = -9

==> t = -9/5

==> x = 2 - 9/5 = 1/5

==> y = 1 + 2(-9/5) = -13/5

==> z = 3 - 9/5 = 6/5

Hence point of intersection is (1/5 , -13/5 , 6/5)