Given $\mathbf { u } = \langle - 5 , - 6 \rangle$ and $\mathbf { v } = \langle - 6 , - 5 \rangle$ ,find $$u^.v$$ .
A)0
B)30
C)60
D)61
E)-11

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 $\mathbf{u} = \langle -5, -6 \rangle$ and $\mathbf{v} = \langle -6, -5 \rangle$, the dot product is $(-5) \cdot (-6) + (-6) \cdot (-5) = 30 + 30 = 60$.

Given u=⟨−5,−6⟩\mathbf { u } = \langle - 5 , - 6 \rangleu=⟨−5,−6⟩

Given $\mathbf { u } = \langle - 5 , - 6 \rangle$