Determine whether $\mathbf { u }$ and $\mathbf { v }$ are orthogonal, parallel, or neither.
$$\mathbf { u } = \langle - 7,3 \rangle , \mathbf { v } = \langle 12,35 \rangle$$
A) orthogonal
B) parallel
C) neither

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product is zero, and they are parallel if one is a scalar multiple of the other. The dot product of $\mathbf { u }$ and $\mathbf { v }$ is $(-7)(12) + (3)(35) = -84 + 105 = 21$, which is not zero, so they are not orthogonal. Also, there is no scalar by which all components of $\mathbf { u }$ can be multiplied to obtain the components of $\mathbf { v }$, so they are not parallel. Therefore, the vectors are neither orthogonal nor parallel.

Determine Whether u\mathbf { u }u And v\mathbf { v }v Are Orthogonal, Parallel, or Neither

Determine Whether $\mathbf { u }$ And $\mathbf { v }$ Are Orthogonal, Parallel, or Neither