Find the plane through the point P = (2, 1, -1) which is perpendicular to the planes 2x + y – z = 3 and x + 2y + z = 2.
So far, what I'm doing is taking the two direction vectors from the 2 given planes (2, 1, -1) and (1, 2, 1) and taking the cross product between them to get (3, 3, 3). I then used this directional derivative to get an equation of a plane through the point (2, 1, -1) like so: 3(x – 2) + 3(y – 1) + 3(z + 1) = 0. However, my answer is x + y + z = 3 and the correct answer is x – y + z = 0. What am I doing wrong?
Best Answer
You made a mistake in the cross product. It should be (3,-3,3).