Q. If the vectors $\overrightarrow{\mathbf{a}} = \widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}},\ \overrightarrow{\mathbf{b}} = 2\widehat{\dot{\mathbf{i}}} + 4\widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$ and $\overrightarrow{\mathbf{c}} = \lambda\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \mu\widehat{\mathbf{k}}$ are mutually orthogonal, then $(\lambda,\mu)$ is equal to
A) $( - 3,2)$
B) $(2, - 3)$
C) $( - 2.3)$
D) $(3, - 2)$
Explanation
(a)
$\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{c}} = 0$
$\Longrightarrow \lambda - 1 + 2\mu = 0$
$\Longrightarrow \lambda + 2\mu = 1$ …(i)
$\overrightarrow{\mathbf{b}} \bullet \overrightarrow{\mathbf{c}} = 0$
$\Longrightarrow 2\lambda + 4 + \mu = 0$
$\Longrightarrow 2\lambda + \mu = - 4$….(ii)
On solving Eqs. (i) and (ii), we get
$\lambda - 3,\mu = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.