Determine whether the planes are parallel,orthogonal,or neither.
5x - 6y - 6z = 0
3x - 4y + 2z = -4
A)parallel
B)orthogonal
C)neither

Question

Determine whether the planes are parallel,orthogonal,or neither. 
5x - 6y - 6z = 0
3x - 4y + 2z = -4
A)parallel
B)orthogonal
C)neither

Quizplus · Accepted Answer

The planes are neither parallel nor orthogonal. To determine this, we compare the direction vectors (normal vectors) of the planes. For the planes given by $5x - 6y - 6z = 0$ and $3x - 4y + 2z = -4$, the direction vectors are $<5, -6, -6>$ and $<3, -4, 2>$, respectively. Parallel planes would have proportional direction vectors, and orthogonal planes would have direction vectors that are dot products equal to zero. The dot product of $<5, -6, -6>$ and $<3, -4, 2>$ is $15 + 24 - 12 = 27$, which is not zero, so they are not orthogonal. Since the ratios of the corresponding components of the vectors are not equal, they are not parallel either.

Determine Whether the Planes Are Parallel,orthogonal,or Neither