3-1.Vectors question bank (Physics)

If $\overrightarrow{A}=3 \hat{\imath}-2 \hat{\jmath}+\hat{k}$,$\overrightarrow{B}=\hat{\imath}-3 \hat{\jmath}+5 \hat{k}$ and $\overrightarrow{C}=2 \hat{\imath}+\hat{\jmath}-4 \hat{k}$ form a right-angled triangle,then which of the following is satisfied?

$A$ vector $\vec{A}$ having magnitude $6$ units is added to vector $\vec{B}$,which is along the $x$-axis. The resultant of $\vec{A}$ and $\vec{B}$ is along the $y$-axis. If the magnitude of the resultant of $\vec{A}$ and $\vec{B}$ is three times that of $\vec{B}$,then the magnitude of $\vec{B}$ is: