Evaluate the expression.
-$$r = \langle 9 , - 9 , - 4 \rangle , \mathbf { v } = \langle 6 , - 9 , - 6 \rangle , \mathbf { w } = \langle 6 , - 1 , - 3 \rangle$$
$( \mathbf { r } + \mathbf { v } ) \cdot \mathbf { w }$
A) 138
B) $\langle - 90 , - 18 , - 30 \rangle$
C) $\langle - 54 , - 81 , - 24 \rangle$
D) $- 138$

Question

Quizplus · Accepted Answer

First, add vectors $\mathbf{r}$ and $\mathbf{v}$: $\mathbf{r} + \mathbf{v} = \langle 9 + 6, -9 - 9, -4 - 6 \rangle = \langle 15, -18, -10 \rangle$. Then, dot this result with $\mathbf{w}$: $\langle 15, -18, -10 \rangle \cdot \langle 6, -1, -3 \rangle = (15 \times 6) + (-18 \times -1) + (-10 \times -3) = 90 + 18 + 30 = 138$.

Evaluate the Expression r=⟨9,−9,−4⟩,v=⟨6,−9,−6⟩,w=⟨6,−1,−3⟩r = \langle 9 , - 9 , - 4 \rangle , \mathbf { v } = \langle 6 , - 9 , - 6 \rangle , \mathbf { w } = \langle 6 , - 1 , - 3 \rangler=⟨9,−9,−4⟩,v=⟨6,−9,−6⟩,w=⟨6,−1,−3⟩

Evaluate the Expression $r = \langle 9 , - 9 , - 4 \rangle , \mathbf { v } = \langle 6 , - 9 , - 6 \rangle , \mathbf { w } = \langle 6 , - 1 , - 3 \rangle$