Question

The vector $a\hat{i}+b\hat{j}+c\hat{k}$ is a bisector of the angle between the vectors $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}$ if

• A. a=b
• B. a=c
• C. c=a+b
• D. a =b=c

Answer 1

The correct option is B a=c

$a\hat{i}+b\hat{j}+c\hat{k}$=Angle bisector of $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}=m$ $\left[\frac{\hat{i}+\hat{j}+\hat{j}+\hat{k}}{\sqrt{2}}\right]\Rightarrow a=\frac{m}{\sqrt{2}},b=\sqrt{2}.m,c=\frac{m}{\sqrt{2}}$