Question

Linear algebra help please!

Determine the values of the parameter (alpha) the following planes in R^3 are perpendicular:

(alpha)x+10y-8z=2
(alpha)x+(alpha)y-2z=-11

Answer 1

If their normal vectors are orthogonal, the planes are as well.

Answer 2

\[
\begin{bmatrix}
\alpha \\ 10 \\-8
\end{bmatrix}
\cdot
\begin{bmatrix}
\alpha \\ \alpha \\-2
\end{bmatrix}
=
0
\]

Answer 3

Great!!! Thank you so much! I'd give you an eggroll if you were here :D