Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \langle - 4 , - 7 \rangle , \mathbf { v } = \langle 14,24 \rangle$
A)orthogonal
B)parallel
C)neither

Question

Quizplus · Accepted Answer

Two vectors are orthogonal if their dot product is zero, and parallel if one is a scalar multiple of the other. The dot product of $\mathbf{u}$ and $\mathbf{v}$ is $(-4)(14) + (-7)(24) = -56 - 168 = -224$, which is not zero, so they are not orthogonal. They are not parallel either because there is no scalar $k$ such that $\mathbf{u} = k\mathbf{v}$; specifically, $-4/14 \neq -7/24$. Therefore, the vectors are neither orthogonal nor parallel.

Determine Whether U Are V and Orthogonal, Parallel, or Neither u=⟨−4,−7⟩,v=⟨14,24⟩\mathbf { u } = \langle - 4 , - 7 \rangle , \mathbf { v } = \langle 14,24 \rangleu=⟨−4,−7⟩,v=⟨14,24⟩

Determine Whether U Are V and Orthogonal, Parallel, or Neither $\mathbf { u } = \langle - 4 , - 7 \rangle , \mathbf { v } = \langle 14,24 \rangle$