Question

The unit vector perpendicular to vectors $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$ forming a right handed system is

• A. k
• B. 2k
• C. -k
• D. None of these

Answer 1

Answer: (C)

Let the required vector be $a$. Then, $I+J,I-J$ and $a$ form a right handed system
$\therefore a=(i+j)\times (i-j)$
$=\left|\begin{array}{ccc}i& j& k\\ 1& 1& 0\\ 1& -1& 0\end{array}\right|$
$=i(0-0)-j(0-0)+k(-1-1)$
$=-2k$
Hence, the required unit vector is
$a=\frac{a}{|a|}=\frac{-2k}{|-2k|}=\frac{-2k}{\sqrt{4}}=-k$