10. vector algebra — ગણિત ધોરણ 12 સાયન્સ — Question

$\vec{b}=2 \hat{i}+4 \hat{j}+4 \hat{k} ,$

$\vec{c}=\lambda \hat{i}+\hat{j}+\mu \hat{k} $

$\vec{a}$ and $\vec{c}$ are orthogonal $\Rightarrow \vec{a} \cdot \vec{c}=0$ giving $\lambda-1+2 \mu=0$

Also $\vec{b}$ and $\vec{c}$ are orthogonal $\Rightarrow 2 \lambda+4+4 \mu=0$

Solving the equation we get $\lambda=-3, \mu=2$