Question

Find the vector which acts like the angle bisector for the vectors $2\hat{i}+2\hat{j}+\hat{k}and2\hat{i}+4\hat{j}+\sqrt{5}\hat{k}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

As we know the bisector will lie along
$\frac{\overline{a}}{|a|}+\frac{\overline{b}}{|b|}$
$Here,\overline{a}=2\hat{i}+2\hat{j}+\hat{k}and\overline{b}=2\hat{i}+4\hat{j}+\sqrt{5}\hat{k}$

$\therefore Anglebisector=\frac{2\hat{i}+2\hat{j}+\hat{k}}{\sqrt{4+4+1^2}}+\frac{2\hat{i}+4\hat{j}+\sqrt{5}\hat{k}}{\sqrt{2^2+4^2+\sqrt{5^2}}}$
$=\frac{2\hat{i}+2\hat{j}+\hat{k}}{3}+\frac{2\hat{i}+4\hat{j}+3\hat{k}}{\sqrt{25}}=\frac{10\hat{i}+10\hat{j}+5\hat{k}+6\hat{i}+12\hat{j}+9\hat{k}}{15}=\frac{16\hat{i}+22\hat{j}+14\hat{k}}{15}$ $\therefore$ Answer is hence option (a)