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

Question

Quizplus · Accepted Answer

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 $1 \cdot 1 + \sqrt{3} \cdot (-2) = 1 - 2\sqrt{3}$, which is neither zero (not orthogonal) nor indicates that the vectors are scalar multiples of each other (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 } \mathrm { j } , \quad \mathbf { w } = \mathrm { i } - 2 \mathrm { j }v=i+3​j,w=i−2j

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