Solve the problem.
-If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle - 4,6 \rangle$, and $\mathbf { w } = \langle - 11,2 \rangle$, evaluate $\mathbf { u } \cdot ( \mathbf { v } - \mathbf { w } )$.
A) $- 3$
B) $- 7$
C) $- 12$
D) 20

Question

Quizplus · Accepted Answer

First, find the vector $\mathbf{v} - \mathbf{w}$ by subtracting the corresponding components of $\mathbf{v}$ and $\mathbf{w}$: $\mathbf{v} - \mathbf{w} = \langle -4, 6 \rangle - \langle -11, 2 \rangle = \langle -4 + 11, 6 - 2 \rangle = \langle 7, 4 \rangle$. Then, calculate the dot product $\mathbf{u} \cdot (\mathbf{v} - \mathbf{w}) = \langle -5, 7 \rangle \cdot \langle 7, 4 \rangle = (-5 \times 7) + (7 \times 4) = -35 + 28 = -7$.

Solve the Problem u=⟨−5,7⟩,v=⟨−4,6⟩\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle - 4,6 \rangleu=⟨−5,7⟩,v=⟨−4,6⟩

Solve the Problem $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle - 4,6 \rangle$