Given vectors $\mathbf { u } = \langle - 1 , - 2 \rangle$ and $\mathbf { v } = \langle 3,5 \rangle$ determine the quantity indicated below. $( 4 \mathbf { u } \cdot 2 \mathbf { v } ) \mathbf { u }$
A) $\langle 32,64 \rangle$
B) $\langle 104,208 \rangle$
C) $\langle - 8 , - 16 \rangle$
D) $\langle 8,16 \rangle$
E) $\langle - 64 , - 128 \rangle$

Question

Quizplus · Accepted Answer

First, calculate $4\mathbf{u} = 4\langle -1, -2 \rangle = \langle -4, -8 \rangle$ and $2\mathbf{v} = 2\langle 3, 5 \rangle = \langle 6, 10 \rangle$. Then, find the dot product $4\mathbf{u} \cdot 2\mathbf{v} = \langle -4, -8 \rangle \cdot \langle 6, 10 \rangle = (-4)(6) + (-8)(10) = -24 - 80 = -104$. Finally, multiply this scalar by $\mathbf{u}$ to get $(-104)\mathbf{u} = (-104)\langle -1, -2 \rangle = \langle 104, 208 \rangle$.

Given Vectors u=⟨−1,−2⟩\mathbf { u } = \langle - 1 , - 2 \rangleu=⟨−1,−2⟩

Given Vectors $\mathbf { u } = \langle - 1 , - 2 \rangle$