Let overline{OA}=overline{a}, overline{OB}=ov | vedclass

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Question

(A) Let $\hat{a} = \frac{\overline{a}}{|\overline{a}|}$ and $\hat{b} = \frac{\overline{b}}{|\overline{b}|}$ be the unit vectors along $\overline{OA}$

Vedclass · Accepted Answer

$x-y=0$

Vedclass · Answer

(A) Let $\hat{a} = \frac{\overline{a}}{|\overline{a}|}$ and $\hat{b} = \frac{\overline{b}}{|\overline{b}|}$ be the unit vectors along $\overline{OA}$ and $\overline{OB}$ respectively.The angle bisector of $\angle AOB$ is along the direction of the sum of the unit vectors,which is $\hat{a} + \hat{b}$.Given that the vector along the angle bisector is $x\hat{a} + y\hat{b}$,we have $x\hat{a} + y\hat{b} = k(\hat{a} + \hat{b})$ for some scalar $k 
eq 0$.Comparing the coefficients of $\hat{a}$ and $\hat{b}$,we get $x = k$ and $y = k$.Therefore,$x = y$,which implies $x - y = 0$.

Let $\overline{OA}=\overline{a}, \overline{OB}=\overline{b}$. If the vector along the angle bisector of $\angle AOB$ is given by $x \frac{\overline{a}}{|\overline{a}|}+y \frac{\overline{b}}{|\overline{b}|}$,then which of the following is true?

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