Question

The rectangular components of a vector are $(2,2).$ The corresponding rectangular components of another vector are $(1,\sqrt{3}).$ Find the angle between the two vectors.

• A. $\frac{5\pi }{12}$
• B. $\frac{\pi }{12}$
• C. $\frac{3\pi }{12}$
• D. $\frac{\pi }{24}$

Answer 1

The correct option is B $\frac{\pi }{12}$

let $\overrightarrow{a}$=(2,2) and b=$1,\sqrt{3}$

we need the angle between the two vectors let angle be \theta Then

$\overrightarrow{a}$.$\overrightarrow{b}$=abcos\theta

so $2+\sqrt{3}$=$(2,\sqrt{2})$(2)$cos\theta$

so,$cos\theta$=$\frac{1+\sqrt{3}}{2\sqrt{2}}$

so $\theta$=$co{s}^{-1}\frac{1+\sqrt{3}}{2\sqrt{2}}$ $=\frac{\pi }{12}$