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

To determine whether two vectors are orthogonal, we need to compute their dot product. If the dot product is zero, the vectors are orthogonal. However, if the dot product is nonzero, we cannot conclude that the vectors are parallel or neither without further computation. In this case, the dot product of $\mathbf{u}$ and $\mathbf{v}$ is
$$\mathbf{u}\cdot\mathbf{v}=(-7)\cdot(12)+(3)\cdot(35)=-84+105=21\neq 0,$$
so $\mathbf{u}$ and $\mathbf{v}$ are neither orthogonal nor parallel. Therefore, the answer is $\boxed{\text{(C)}}$.

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