# If $\overrightarrow a=\hat i-\hat j+2\hat k, \:\:\overrightarrow b=2\hat i+4\hat j+\hat k\:\:and\:\:\overrightarrow c=\lambda \hat i+\hat j+\mu k$ are mutually $\perp$ then $(\lambda,\mu)=?$

$\begin{array}{1 1} (-3,2) \\ (2,-3) \\ (-2,3) \\ (3,-2) \end{array}$

Since $\overrightarrow a,\:\overrightarrow b\:and\:\overrightarrow c$ are mutually $\perp$,
$\overrightarrow a.\overrightarrow b=\overrightarrow b.\overrightarrow c=\overrightarrow c.\overrightarrow a=0$
$\Rightarrow\:\lambda-1+2\mu=0\:\:and\:\:2\lambda+4+\mu=0$
Solving which we get $\lambda=-3\:\:and\: \mu=2$