Question

If $\vec{a}$ and $\vec{b}$ are two unit vectors inclined to $x$-axis at angles $30^{°}$ and $120^{°}$ respectively, then $\left|\vec{a}+\vec{b}\right|$ equals

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

Answer 1

Answer: (B)

Clearly, angle between $\vec{a}$ and $\vec{b}=\frac{\pi }{2}$
$\Rightarrow \vec{a}\cdot \vec{b}=0$
$\therefore {\left|\vec{a}+\vec{b}\right|}^2={\left|\vec{a}\right|}^2+{\left|\vec{b}\right|}^2+2\vec{a}\cdot \vec{b}$
$=1+1+0=2$
$\Rightarrow \left|\vec{a}+\vec{b}\right|=\sqrt{2}$