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

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product is zero. The dot product of $\mathbf{v}$ and $\mathbf{w}$ is $4\cdot1 + 1\cdot(-4) = 4 - 4 = 0$, indicating they are orthogonal.

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

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