Determine whether the planes are parallel,orthogonal,or neither.
5x - 4y + z = -2
3x + 4y + z = -5
A)parallel
B)orthogonal
C)neither

Question

Determine whether the planes are parallel,orthogonal,or neither. 
5x - 4y + z = -2
3x + 4y + z = -5
A)parallel
B)orthogonal
C)neither

Quizplus · Accepted Answer

Two planes are orthogonal if and only if their normal vectors are orthogonal. The normal vector of the first plane is (5, -4, 1) and the normal vector of the second plane is (3, 4, 1). The dot product of these two vectors is (5)(3) + (-4)(4) + (1)(1) = 15 - 16 + 1 = 0. Thus, the planes are orthogonal.

Determine Whether the Planes Are Parallel,orthogonal,or Neither