Question

Given the vectors $u=[-5,4]$ and $v=[3,-1],|2u-3v|=$

• A. $[19,11]$
• B. $\sqrt{482}$
• C. $[19,13]$
• D. $2\sqrt{41}-3\sqrt{10}$
• E. $2\sqrt{65}$

Answer 1

The correct option is B $\sqrt{482}$

Since the vectors $u=[-5,4]$ and $v=[3,-1]$, we calculate $2u-3v$ as shown below:

$2u-3v=\left[2\right(-5)-3(3),2(4)-3(-1\left)\right]=[-10-9,8+3]=[-19,11]$

Now the distance from the origin to the end of the vector $|2u-3v|$ is as follows:

$\sqrt{(-19{)}^2+{11}^2}=\sqrt{361+121}=\sqrt{482}$