Determine whether $\mathbf { u }$ and $\mathbf { v }$ are orthogonal, parallel, or neither.
$$\mathbf { u } = \langle 1 , - 5 \rangle , \mathbf { v } = \langle 20,3 \rangle$$
A) orthogonal
B) parallel
C) neither

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product is zero, and parallel if one is a scalar multiple of the other. The dot product of $\mathbf{u}$ and $\mathbf{v}$ is $1(20) + (-5)(3) = 20 - 15 = 5$, which is not zero, so they are not orthogonal. Since there is no scalar $k$ such that $k\langle 1, -5 \rangle = \langle 20, 3 \rangle$, they are not parallel either. 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