Question

Find a nonzero vector orthogonal to the plane through the points p(0, -2, 0), q(6, 1, -2), and r(5, 2, 1).

Answer 1

To find a nonzero vector orthogonal to a plane through given points P, Q, and R, we subtract the coordinates of two points to obtain two vectors and then calculate their cross product.

Step-by-step explanation:

To find a nonzero vector orthogonal to a plane, we need to find the cross product of two vectors in the plane. The two vectors can be obtained by subtracting the coordinates of two points in the plane.

1. Let vector PQ be the difference between points P and Q, and vector PR be the difference between points P and R.
2. Calculate the cross product of vectors PQ and PR to obtain the desired vector. The cross product is given by (PQ) x (PR).
3. Simplify the cross product to obtain the nonzero vector orthogonal to the plane through the given points.