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

To determine whether two vectors are orthogonal, we need to compute their dot product. If the dot product is zero, then the vectors are orthogonal. Otherwise, they are not orthogonal. 
$\mathbf{u}\cdot\mathbf{v}=(1)(20)+(-5)(3)=20-15=5
eq0$, therefore $\mathbf{u}$ and $\mathbf{v}$ are not orthogonal.

To determine whether two vectors are parallel, we can compare their direction. If the direction of one vector is a scalar multiple of the other vector, then they are parallel. Otherwise, they are not parallel.

$\mathbf{u}=\langle 1,-5angle$ has a direction of $\frac{-5}{1}=-5$.

$\mathbf{v}=\langle 20,3angle$ has a direction of $\frac{3}{20}$.

Since these directions are not equal, the vectors are not parallel. Therefore, the answer is C (neither).

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