Question

Find parametric equations for the line through the point (0, 2, 2) that is parallel to the plane x + y + z = 4 and perpendicular to the line x = 1 + t, y = 2 − t, z = 2t.

Answer 1

Answer: X = 3t, Y =2 - t, Z =2

Step-by-step explanation: the plane

x + y + z =4has normal vector

M =<1,1,1> and the line

x = 1 + t, y = 2 − t, z = 2t has direction

v =<1, −1, 2>. So the vector

A= n × v

=<1, 1, 1> × <1, −1, 2>

=<2−(−1),1−2,−1−1>

=<3,−1,−2>