Given $\mathbf { u } = \langle - 3,7 \rangle$ and $\mathbf { v } = \langle 1 , - 5 \rangle$, find $\mathbf { u } \cdot \mathbf { v }$.
A) 32
B) $- 3$
C) $- 38$
D) 22
E) 8

Question

Quizplus · Accepted Answer

The dot product of two vectors $\mathbf{u} = \langle a, b \rangle$ and $\mathbf{v} = \langle c, d \rangle$ is calculated as $a \cdot c + b \cdot d$. For $\mathbf{u} = \langle -3, 7 \rangle$ and $\mathbf{v} = \langle 1, -5 \rangle$, the dot product is $(-3) \cdot 1 + 7 \cdot (-5) = -3 - 35 = -38$.

Given u=⟨−3,7⟩\mathbf { u } = \langle - 3,7 \rangleu=⟨−3,7⟩ And v=⟨1,−5⟩\mathbf { v } = \langle 1 , - 5 \ranglev=⟨1,−5⟩

Given $\mathbf { u } = \langle - 3,7 \rangle$ And $\mathbf { v } = \langle 1 , - 5 \rangle$