Question

Distance between the following pairs of points in the ascending order is
$A\left)\right(-3,{45}^{\circ }),(7,{105}^{\circ })$
$B\left)\right(\sqrt{2},\frac{\pi }{4}),(2,\frac{\pi }{2})$
$C\left)\right(3,\frac{\pi }{6}),(7,\frac{\pi }{6})$

• A. B, C, A
• B. B, A, C
• C. A, C, B
• D. A, B, C

Answer 1

The correct option is A B, C, A

Distance between two points is
$d=\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos ({\theta }_1-{\theta }_2)}$
A) Points are $(-3,{45}^0),(7,{105}^0)$
$d_1=\sqrt{9+49+42\cos (-{60}^0)}$
$\Rightarrow d_1=\sqrt{79}$
B)Points are $(\sqrt{2},\frac{\pi }{4}),(2,\frac{\pi }{2})$
$d_2=\sqrt{2+4-4\sqrt{2}\cos (-\frac{\pi }{4})}$
$d_2=\sqrt{2}$
C) Points are $(3,\frac{\pi }{6}),(7,\frac{\pi }{6})$
$d_3=\sqrt{9+49-42\cos \left(0\right)}$
$d_3=4$
So, arranging the distances in ascending order
$d_2,d_3,d_1$ or B C A