Question

Find out the unit vector perpendicular to both vectors

$\widehat{i}–\widehat{j} + \widehat{k}$ and $\widehat{i} + \widehat{j} + \widehat{k}$.

• A. (a)$\widehat{i} + \widehat{j}$
• A. (b)$\frac{- \widehat{i} + \widehat{k}}{\sqrt{2}}$
• A. (c)$\widehat{j} + \widehat{k}$
• A. (d)$\frac{\widehat{i} + \widehat{j}}{\sqrt{2}}$

Answer 1

(b)

$\overset{\rightarrow}{a} \times \overset{\rightarrow}{b}$ = $\left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 1 & - 1 & 1 \\ 1 & 1 & 1 \end{matrix} \right|$ =$- 2\widehat{i} + 2\widehat{k}$

here $\overset{\rightarrow}{a} \times \overset{\rightarrow}{b}$ is perpendicular to both $\overset{\rightarrow}{a}and\overset{\rightarrow}{b}$ unit vector

along $\overset{\rightarrow}{a} \times \overset{\rightarrow}{b}$= $\frac{- 2\widehat{i} + 2\widehat{k}}{\sqrt{(–2)^{2} + 2^{2}}}$

= $\frac{- \widehat{i} + \widehat{k}}{\sqrt{2}}$