Question

If the vectors $\vec{a} = \hat{i}- \hat{j}+2 \hat{k}, \vec{b} = 2\hat{i}+4 \hat{j}+ \hat{k}$ and $\vec{c} = \lambda\hat{i}+ \hat{j}+\mu \hat{k}$ are mutually orthogonal, then $\left(\lambda, \mu\right) = $

• A. (2, -3)
• B. (-2, 3)
• C. (3, -2)
• D. (-3, 2)

Answer 1

Answer: (D)

$\vec{a} \cdot\vec{b} = 0, \quad\vec{b} \cdot \vec{c} = 0, \quad\vec{c} \cdot \vec{a} = 0$
$\Rightarrow 2\lambda + 4 + \mu = 0\quad\lambda - 1+2\mu = 0$
Solving we get: $\lambda = -3, \,\mu = 2$