Determine whether the planes are parallel,orthogonal,or neither. 5x - y + z = -4
-x - 6y - z = -2
A)neither
B)orthogonal
C)parallel

Question

Quizplus · Accepted Answer

The planes are orthogonal (perpendicular) because the dot product of their normal vectors is equal to zero. The normal vectors are (5,-1,1) and (-1,-6,-1), so their dot product is (5)(-1) + (-1)(-6) + (1)(-1) = -5 + 6 - 1 = 0. Therefore, the planes are orthogonal.

Determine Whether the Planes Are Parallel,orthogonal,or Neither