When vector A → = 2 i ^ + 3 j ^ + 2 k ^ is subtracted from vector B → , it gives a vector equal…

It is given that $\overrightarrow{A}=2\hat{i}+3\hat{j}+2\hat{k}$.

By the given condition,

 $\overrightarrow{B}-(2\hat{i}+3\hat{j}+2\hat{k})=2\hat{j}$

 $\Rightarrow \overrightarrow{B}=2\hat{i}+5\hat{j}+2\hat{k}$ 

The magnitude is given by the formula,$\left|\overrightarrow{B}\right|=\sqrt{{B^2}_x+{B^2}_y+{B^2}_z}$
 $\Rightarrow \left|\overrightarrow{B}\right|=\sqrt{4+25+4}=\sqrt{33}$