Let a and b be two unit vectors and θ is the angle between them. … - Vidyadip

Question

Let $\vec a$ and $\vec b$ be two unit vectors and θ is the angle between them. Then $\vec a + \vec b$ is a unit vector if

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Answer

It is given that $|\vec a|=|\vec b|=1$
$\therefore |\vec a+\vec b|^2=(\vec a+\vec b).(\vec a+\vec b)=|\vec a|^2+|\vec b|^2+2\vec a.\vec b$
$\Rightarrow |\vec a+\vec b|^2=1+1+2|\vec a||\vec b|cos\theta=2+2cos\theta$
It is given that $(\vec a+\vec b)$ is a unit vector.
Therefore, 2 + 2$cos\theta$ = 1
Therefore, $\theta=\frac{2\pi}{3}$

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