State whether the vectors are parallel, orthogonal, or neither.
-$$\mathbf { v } = \mathrm { i } + \sqrt { 3 } \mathbf { j } , \quad \mathbf { w } = \mathrm { i } - 2 \mathbf { j }$$
A) Parallel
B) Orthogonal
C) Neither

Question

Quizplus · Accepted Answer

To determine the relationship between the vectors $\mathbf{v} = \mathrm{i} + \sqrt{3}\mathbf{j}$ and $\mathbf{w} = \mathrm{i} - 2\mathbf{j}$, we can use the dot product. The dot product of $\mathbf{v}$ and $\mathbf{w}$ is $(1)(1) + (\sqrt{3})(-2) = 1 - 2\sqrt{3}$, which is not zero, indicating the vectors are not orthogonal. Since the ratios of the corresponding components are not equal (i.e., $1/1 \neq \sqrt{3}/-2$), the vectors are not parallel. Therefore, the vectors are neither parallel nor orthogonal.

State Whether the Vectors Are Parallel, Orthogonal, or Neither v=i+3j,w=i−2j\mathbf { v } = \mathrm { i } + \sqrt { 3 } \mathbf { j } , \quad \mathbf { w } = \mathrm { i } - 2 \mathbf { j }v=i+3​j,w=i−2j

State Whether the Vectors Are Parallel, Orthogonal, or Neither $\mathbf { v } = \mathrm { i } + \sqrt { 3 } \mathbf { j } , \quad \mathbf { w } = \mathrm { i } - 2 \mathbf { j }$