Question

If the difference of two unit vectors is again a unit vector, then the angle between them is

• A. 30$^\circ$
• B. 45$^\circ$
• C. 60$^\circ$
• D. 90$^\circ$

Answer 1

Answer: (C)

60$^\circ$

Answer 2

Let $\vec{a}-\vec{b}=\vec{c}$ where $\vec{a}$, $\vec{b}$, $\vec{c}$ are unit vectors. $\therefore \left(\vec{a}-\vec{b}\right)^{2}=\vec{c}^{2}$ $\Rightarrow a^{2}+b^{2}-2\,\vec{a} . \vec{b}=c^{2}$ $\Rightarrow 1+1-2 \left(ab\,cos\,\theta\right)=1$ $\Rightarrow 2\left(1\right)\left(1\right)\,cos\,\theta=1$ $\Rightarrow cos\,\theta=\frac{1}{2}$ $\Rightarrow \theta=60^{\circ}$