Solve the problem.
-If $\mathbf { u } = \langle - 5,3 \rangle , \mathbf { v } = \langle 3 , - 6 \rangle$, and $\mathbf { w } = \langle - 3,12 \rangle$, evaluate $\mathbf { u } \cdot \mathbf { w } + \mathbf { v } \cdot \mathbf { w }$.
A) $- 25$
B) $- 23$
C) $- 30$
D) $- 34$

Question

Quizplus · Accepted Answer

The dot product of two vectors $\mathbf{a} = \langle a_1, a_2 \rangle$ and $\mathbf{b} = \langle b_1, b_2 \rangle$ is given by $\mathbf{a} \cdot \mathbf{b} = a_1b_1 + a_2b_2$. Thus, $\mathbf{u} \cdot \mathbf{w} = (-5)(-3) + (3)(12) = 15 + 36 = 51$ and $\mathbf{v} \cdot \mathbf{w} = (3)(-3) + (-6)(12) = -9 - 72 = -81$. Adding these gives $51 + (-81) = -30$.

Solve the Problem u=⟨−5,3⟩,v=⟨3,−6⟩\mathbf { u } = \langle - 5,3 \rangle , \mathbf { v } = \langle 3 , - 6 \rangleu=⟨−5,3⟩,v=⟨3,−6⟩

Solve the Problem $\mathbf { u } = \langle - 5,3 \rangle , \mathbf { v } = \langle 3 , - 6 \rangle$