Determine whether the planes are parallel, orthogonal, or neither.
$$\begin{array} { l }
6 x - y - z = 4 \
24 x - 4 y - 4 z = 18
\end{array}$$
A) parallel
B) orthogonal
C) neither

Question

Determine whether the planes are parallel, orthogonal, or neither.
$$\begin{array} { l } 
6 x - y - z = 4 \
24 x - 4 y - 4 z = 18
\end{array}$$
A) parallel
B) orthogonal
C) neither

Quizplus · Accepted Answer

Parallel planes have normal vectors that are scalar multiples of each other. The normal vector of the first plane is $6\mathbf{i} - \mathbf{j} - \mathbf{k}$ and of the second plane is $24\mathbf{i} - 4\mathbf{j} - 4\mathbf{k}$, which is $4$ times the first, indicating the planes are parallel.

Determine Whether the Planes Are Parallel, Orthogonal, or Neither 6x−y−z=424x−4y−4z=18\begin{array} { l } 6 x - y - z = 4 \\24 x - 4 y - 4 z = 18\end{array}6x−y−z=424x−4y−4z=18​

Determine Whether the Planes Are Parallel, Orthogonal, or Neither $\begin{array} { l } 6 x - y - z = 4 \\24 x - 4 y - 4 z = 18\end{array}$