Determine whether u are v and orthogonal,parallel,or neither. $$\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangle$$
A)neither
B)orthogonal
C)parallel

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product equals zero, and parallel if one is a scalar multiple of the other. The dot product of $\mathbf{u}$ and $\mathbf{v}$ is $(-1)(-10) + (5)(-3) = 10 - 15 = -5$, which is not zero, so they are not orthogonal. They are not parallel either because there is no scalar $k$ such that $\mathbf{u} = k\mathbf{v}$ or $\mathbf{v} = k\mathbf{u}$. Therefore, the vectors are neither orthogonal nor parallel.

Determine Whether U Are V and Orthogonal,parallel,or Neither u=⟨−1,5⟩,v=⟨−10,−3⟩\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangleu=⟨−1,5⟩,v=⟨−10,−3⟩

Determine Whether U Are V and Orthogonal,parallel,or Neither $\mathbf { u } = \langle - 1,5 \rangle , \mathbf { v } = \langle - 10 , - 3 \rangle$