$\text { Express the vector in the form } v = v _ { 1 } i + v _ { 2 } j + v _ { 3 } k \text {. }$
-$7 \mathbf { u } - 5 \mathbf { v } \text { if } \mathbf { u } = \langle 1,1,0 \rangle \text { and } \mathbf { v } = \langle 3,0,1 \rangle$
A) v = -8i + 12j - 5k
B) v = 22i + 7j - 5k
C) v = 7i + 7j - 5k
D) v = -8i + 7j - 5k

Question

Quizplus · Accepted Answer

We have to subtract 5 times the vector $\mathbf{v}$ from 7 times the vector $\mathbf{u}$:
\begin{align*}
7\mathbf{u}-5\mathbf{v}&=7\langle1,1,0angle-5\langle3,0,1angle\
&=\langle7,7,0angle+\langle-15,0,-5angle\
&=\langle-8,7,-5angle.
\end{align*}
Therefore, the vector can be expressed as $-8\mathbf{i}+7\mathbf{j}-5\mathbf{k}$, which corresponds to choice D.

Express the vector in the form v=v1i+v2j+v3k. \text { Express the vector in the form } v = v _ { 1 } i + v _ { 2 } j + v _ { 3 } k \text {. } Express the vector in the form v=v1​i+v2​j+v3​k.

$\text { Express the vector in the form } v = v _ { 1 } i + v _ { 2 } j + v _ { 3 } k \text {. }$