If $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$ and $\mathbf { v } = - 6 \mathbf { i } + 5 \mathbf { j }$ , find $\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }$ .
A) $\mathbf { w } = - 39 \mathbf { i } + 43 \mathbf { j }$
B) $\mathbf { w } = - 33 \mathbf { i } + 43 \mathbf { j }$
C) $\mathbf { w } = - 27 \mathbf { i } + 55 \mathbf { j }$
D) $\mathbf { w } = - 39 \mathbf { i } + 45 \mathbf { j }$
E) $\mathbf { w } = 16 \mathbf { i } - 12 \mathbf { j }$

Question

If $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$ and $\mathbf { v } = - 6 \mathbf { i } + 5 \mathbf { j }$ , find $\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }$ .
A)  $\mathbf { w } = - 39 \mathbf { i } + 43 \mathbf { j }$
B)  $\mathbf { w } = - 33 \mathbf { i } + 43 \mathbf { j }$
C)  $\mathbf { w } = - 27 \mathbf { i } + 55 \mathbf { j }$
D)  $\mathbf { w } = - 39 \mathbf { i } + 45 \mathbf { j }$
E)  $\mathbf { w } = 16 \mathbf { i } - 12 \mathbf { j }$

Quizplus · Accepted Answer

To find $\mathbf { w } = 3 \mathbf { u } + 5 \mathbf { v }$, first calculate $3\mathbf{u} = 3(-3\mathbf{i} + 6\mathbf{j}) = -9\mathbf{i} + 18\mathbf{j}$ and $5\mathbf{v} = 5(-6\mathbf{i} + 5\mathbf{j}) = -30\mathbf{i} + 25\mathbf{j}$. Adding these results gives $\mathbf{w} = -9\mathbf{i} + 18\mathbf{j} - 30\mathbf{i} + 25\mathbf{j} = -39\mathbf{i} + 43\mathbf{j}$.

If u=−3i+6j\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }u=−3i+6j

If $\mathbf { u } = - 3 \mathbf { i } + 6 \mathbf { j }$