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Question

If $$\bar{a}$$ and $$\bar{b}$$ are two unit vectors and $$\theta $$ is the angle between them, then the unit vector along their angular bisector is


A
¯a¯b2cosθ2
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B
¯a+¯b2cosθ2
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C
¯a¯bcosθ2
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D
¯a+¯bcosθ2
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Solution

The correct option is C $$\displaystyle \dfrac{\bar{a}+\bar{b}}{2\cos \dfrac{\theta }{2}}$$
Vector in the direction of angle bisector of $$\bar{a}$$ and $$\bar{b}$$ is $$\displaystyle \frac{\bar{a}+\bar{b}}{2}$$
It has the magnitude $$\cos \dfrac{\theta}{2}$$
$$\therefore $$ Unit vector along direction of angular bisector $$\displaystyle \dfrac{\bar{a}+\bar{b}}{2\cos \dfrac{\theta }{2}}$$

Physics

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