Vector Algebra Question 75
Question: Which one of the following is the unit vector perpendicular to both $ \vec{a}=-\hat{i}+\hat{j}+\hat{k} $ and $ \vec{b}=\hat{i}-\hat{j}+\hat{k} $ ?
Options:
A) $ \frac{\hat{i}+\hat{j}}{\sqrt{2}} $
B) $ \hat{k} $
C) $ \frac{\hat{j}+\hat{k}}{\sqrt{2}} $
D) $ \frac{\hat{i}-\hat{j}}{\sqrt{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] According to question $ a=-\hat{i}+\hat{j}+\hat{k} $ and $ b=\hat{i}-\hat{j}+\hat{k} $ Then, $ a\times b= \begin{vmatrix} i & j & k \\ -1 & 1 & 1 \\ 1 & -1 & 1 \\ \end{vmatrix} $ $ =\hat{i}[1+1]-\hat{j}[-1-1]+\hat{k}[1-1] $ $ =2\hat{i}+2j+0=2(i+j) $ and $ |a\times b|=\sqrt{4+4}=2\sqrt{2} $
$ \therefore $ Required unit vector $ =\pm \frac{2(i+j)}{2\sqrt{2}}=\pm \frac{i+j}{\sqrt{2}} $
BETA
