Question

If $\overline{a}=\overline{i}+\overline{j}+\overline{k},\overline{b}=2\overline{i}-3\overline{j}+\overline{k}$, then $\frac{\overline{a}\times \overline{b}}{|\overline{a}\times \overline{b}|}+\frac{\overline{b}\times \overline{a}}{|\overline{b}\times \overline{a}|}=$

• A. $\overline{0}$
• B. $2\overline{i}+\overline{j}-2\overline{k}$
• C. $\overline{i}+\overline{j}+2\overline{k}$
• D. $\overline{i}+2\overline{j}-\overline{k}$

Answer 1

Answer: (A)

$\overline{0}$

$\overline{a}\times \overline{b}=-(\overline{b}\times \overline{a})$
Also, $|\overline{a}\times \overline{b}|=|(\overline{b}\times \overline{a})|$
Thus, the denominators become equal and the numerator adds up to $0$.
Hence the answer becomes $0$.