Question

If sum of two unit vectors is also an unit vector, then the angle between the two vectors is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{2\pi }{3}$

Answer 1

Answer: (D)

Let $\vec{a}$ and $\vec{b}$ be two unit vectors $\therefore |\vec{a}|=|\vec{b}|=1$ Now, $|\vec{a}+\vec{b}{|}^2=1$ (given) $|\vec{a}{|}^2+|\vec{b}{|}^2+2\vec{a}\cdot \vec{b}=1$ $2\vec{a}\cdot \vec{b}=1-1-1=-1$ $\vec{a}\cdot \vec{b}=\frac{-1}{a^2}$ $\begin{array}{l}\therefore |\vec{a}|\cdot |\vec{b}|\cos \theta =-\frac{1}{2}\\ \Rightarrow \theta =\frac{2\pi }{3}\end{array}$