Question

The angle between the lines $3x+y-7=0$ and $x+2y+9=0$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is D $\frac{\pi }{4}$

$3x+y-7=0$ and $x+2y+9=0$

write in the form $y=mx+c$

$i.e.y=-3x+7,y=\frac{-x}{2}-\frac{9}{2}$

$\therefore m_1=-3$ and $m_2\mp -\frac{1}{2}$

$tan(A-B)=\left|\frac{\tan A-\tan B}{1+\tan A\tan B}\right|$

$\left|\frac{-3-(-y_2)}{1+(-3)(-y_2)}\right|$

$=\left|\frac{-5/2}{5/2}\right|=1$

$\therefore$ Angle b/w then is ${\tan }^{-1}\left(1\right)={45}^{\circ }$

$=\frac{\pi }{4}$