Question

The sum of two unit vectors is a unit vector. The magnitude of their difference is

• A. 2
• B. $\sqrt3$
• C. $\sqrt2$
• D. 1

Answer 1

Answer: (B)

$\sqrt3$

Answer 2

Let $\vec{c}=\vec{a}+\vec{b}$ where $\vec{a}, \vec{b}, \vec{c}$ are all unit vectors $\therefore \vec{c}^{2}=\vec{a}^{2}+\vec{b}^{2}+2\,\vec{a}\cdot\vec{b}$ or $1=1+1+2\,\vec{a}\,.\,\vec{b}$ $\Rightarrow2\,\vec{a}\,.\,\vec{b}=-1$ Again $\left|\vec{a}-\vec{b}\right|^{2}=\vec{a}^{2}+\vec{b}^{2}-2\,\vec{a}\,.\,\vec{b}$ $=1+1-\left(-1\right)=3$ $\therefore=\left|\vec{a}-\vec{b}\right|=\sqrt{3}$