Question

Vectors $u$ and $v$ are given by $u=(3,0)$ and $v(1.-4)$. What is the length of vector $w$, given by $w=2u-v$?

• A. $2\sqrt{10}$
• B. $\sqrt{41}$
• C. $6-\sqrt{17}$
• D. $3$
• E. $\sqrt{23}$

Answer 1

The correct option is B $\sqrt{41}$

given vector

$\overrightarrow{u}=3\hat{i}$

$\overrightarrow{v}=\hat{i}-4\hat{j}$

$\overrightarrow{w}=6\hat{i}-(\hat{i}-4\hat{j})$

$\overrightarrow{w}=6\hat{i}-\hat{i}+4\hat{j}$

$\overrightarrow{w}=5\hat{i}+4\hat{j}$

length or magnitude of vector w

$\left|\overrightarrow{w}\right|=\sqrt{5^2+4^2}$

$\left|\overrightarrow{w}\right|=\sqrt{25+16}$

$\left|\overrightarrow{w}\right|=\sqrt{41}$