Identify the planes that are perpendicular. Select the correct answer.
A) $x + 8 y - z = 6 , - 5 x - y - 13 z = 2$
B) $x + 8 y = 6 , - 5 x - y - 13 z = 2$
C) $x - 8 y = 6 , - 5 x - 13 z = 2$
D) $x + 8 y = 6 , - 5 x - 13 z = 2$
E) $8 x - y - z = 6 , - 5 x + y - 13 z = 2$

Question

Quizplus · Accepted Answer

The normal vectors of the planes in option A are perpendicular: $\langle 1, 8, -1 \rangle$ and $\langle -5, -1, -13 \rangle$. Their dot product is zero: $1(-5) + 8(-1) + (-1)(-13) = 0$.

Identify the Planes That Are Perpendicular x+8y−z=6,−5x−y−13z=2x + 8 y - z = 6 , - 5 x - y - 13 z = 2x+8y−z=6,−5x−y−13z=2

Identify the Planes That Are Perpendicular $x + 8 y - z = 6 , - 5 x - y - 13 z = 2$