Question

The distance between $(a,\frac{\pi }{2})$ and $(3a,\frac{\pi }{6})$ is?

• A. $7a$
• B. $\sqrt{7}a$
• C. $2\sqrt{7a}$
• D. $7\sqrt{2a}$

Answer 1

The correct option is B $\sqrt{7}a$

$(a,\pi /2)=\left(a\cos \right(\pi /2),a\sin (pi/2\left)\right)=(0,a)$

$(3a,\pi /6)=\left(3a\cos \right(\pi /6),3a\sin (\pi /6\left)\right)=(\frac{3\sqrt{3}a}{2},\frac{3a}{2})$

Required distance

$\sqrt{{(\frac{3\sqrt{3}a}{2}-0)}^2+{(\frac{3a}{2}-a)}^2}=\sqrt{\frac{27a^2}{4}+\frac{a^2}{4}}$

$=\sqrt{7}a$