Use the Dot Product to Determine if Two Vectors are Orthogonal
-$$\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j } , \quad \mathbf { w } = 8 \mathbf { i } + 4 \mathbf { j }$$
A) parallel
B) orthogonal
C) neither

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product equals zero. The dot product of vectors $\mathbf{v} = 4\mathbf{i} + 2\mathbf{j}$ and $\mathbf{w} = 8\mathbf{i} + 4\mathbf{j}$ is $4*8 + 2*4 = 32 + 8 = 40$, which is not zero. Instead, since $\mathbf{w}$ is a scalar multiple of $\mathbf{v}$, they are parallel.

Use the Dot Product to Determine If Two Vectors Are v=4i+2j,w=8i+4j\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j } , \quad \mathbf { w } = 8 \mathbf { i } + 4 \mathbf { j }v=4i+2j,w=8i+4j

Use the Dot Product to Determine If Two Vectors Are $\mathbf { v } = 4 \mathbf { i } + 2 \mathbf { j } , \quad \mathbf { w } = 8 \mathbf { i } + 4 \mathbf { j }$