D Determine whether $\mathbf { u }$ and $\mathbf { v }$ are parallel, orthogonal, or neither.
$$\mathbf { u } = \langle 5,6 , - 8 \rangle , \mathbf { v } = \langle 10,12 , - 16 \rangle$$
A) parallel
B) orthogonal
C) neither

Question

Quizplus · Accepted Answer

Two vectors are parallel if one is a scalar multiple of the other. We can check if this is true by finding the ratio of corresponding components of each vector.

\begin{align*}
\frac{5}{10} &= \frac{6}{12} = \frac{-8}{-16} \
\frac{u_1}{v_1} &= \frac{u_2}{v_2} = \frac{u_3}{v_3}
\end{align*}

Since the ratios are equal, we can see that $\mathbf{u}$ and $\mathbf{v}$ are parallel.

D Determine Whether u\mathbf { u }u And v\mathbf { v }v

D Determine Whether $\mathbf { u }$ And $\mathbf { v }$