Question

The angle between line: $r[2\cos \theta +5\sin \theta ]=3$ and $r[2\sin \theta -5\cos \theta ]+4=0$ is:

• A. ${30}^0$
• B. ${45}^0$
• C. ${60}^0$
• D. ${90}^0$

Answer 1

The correct option is D ${90}^0$

Given lines are,
$r[2\cos \theta +5\sin \theta ]=3$ and
$r[2\sin \theta -5\cos \theta ]+4=0$
Cartesian form is,
$2x+5y=3$
$2y-5x=-4$
Slopes of these lines are $-\frac{2}{5}$ and $\frac{5}{2}$
Here, product of slopes $=-1$
Thus, the lines are perpendicular.

Hence, angle between them is ${90}^o$.