Q. A unit vector parallel to the intersection of the plane $\overrightarrow{r} \bullet \left( \widehat{i} - \widehat{j} + \widehat{k} \right) = 5$ and $\overrightarrow{r} \bullet \left( 2\widehat{i} + \widehat{j} - 3\widehat{k} \right) = 4$ is
A) $\frac{2\widehat{i} + 5\widehat{j} - 3\widehat{k}}{\sqrt{38}}$
B) $\frac{2\widehat{i} - 5\widehat{j} + 3\widehat{k}}{\sqrt{38}}$
C) $\frac{- 2\widehat{i} - 5\widehat{j} - 3\widehat{k}}{\sqrt{38}}$
D) $\frac{- 2\widehat{i} + 5\widehat{j} - 3\widehat{k}}{\sqrt{38}}$
Explanation
(c)
$\widehat{a} = \pm \frac{{\overrightarrow{n}}_{1} \times {\overrightarrow{n}}_{2}}{\left| {\overrightarrow{n}}_{1} \times {\overrightarrow{n}}_{2} \right|} = \pm \frac{2\widehat{i} + 5\widehat{j} + 3\widehat{k}}{\sqrt{38}}$ (where ${\overrightarrow{n}}_{1}$ and ${\overrightarrow{n}}_{2}$ are normal to the planes)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.