Let $\vec{p}$ and $\vec{q}$ be two unit vectors and $\alpha$ be the angle between them. Then $(\vec{p}+\vec{q})$ will be a unit vector for what value of $\alpha$ ?

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YESPYQ · Accepted Answer

Correct answer: d) $\frac{2\pi }{3}$. Given, $\left|\vec{p}+\vec{q}\right|=\left|\vec{p}\right|=\left|\vec{q}\right|=1$ Now, ${\left|\vec{p}+\vec{q}\right|}^{2}={\left|\vec{p}\right|}^{2}+{\left|\vec{q}\right|}^{2}+2\vec{p}\cdot \vec{q}$ $\Rightarrow {1}^{2}=1+1+2\cos \alpha$ $\Rightarrow 1=2+2\cos \alpha$ $\Rightarrow \cos \alpha =-\frac{1}{2}$ $\Rightarrow \alpha =\frac{2\pi }{3}$

Let \(\vec{p}\) and \(\vec{q}\) be two unit vectors and \(\alpha\) be the angle between them. Then \((\vec{p}+\vec{q})\)…

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