State whether the vectors are parallel, orthogonal, or neither.
-$$\mathbf { v } = 4 \mathbf { i } - 2 \mathbf { j } , \quad \mathbf { w } = 4 \mathbf { i } + 2 \mathbf { j }$$
A) Orthogonal
B) Parallel
C) Neither

Question

Quizplus · Accepted Answer

Two vectors are parallel if they are scalar multiples of each other, and orthogonal if their dot product is zero. The dot product of $\mathbf{v}$ and $\mathbf{w}$ is $4*4 + (-2)*2 = 16 - 4 = 12$, which is not zero, so they are not orthogonal. They are not scalar multiples of each other because the signs of their $j$ components are different, so they are not parallel either. Therefore, the vectors are neither parallel nor orthogonal.

State Whether the Vectors Are Parallel, Orthogonal, or Neither v=4i−2j,w=4i+2j\mathbf { v } = 4 \mathbf { i } - 2 \mathbf { j } , \quad \mathbf { w } = 4 \mathbf { i } + 2 \mathbf { j }v=4i−2j,w=4i+2j

State Whether the Vectors Are Parallel, Orthogonal, or Neither $\mathbf { v } = 4 \mathbf { i } - 2 \mathbf { j } , \quad \mathbf { w } = 4 \mathbf { i } + 2 \mathbf { j }$