Angle between the lines 2x - y - 15 = 0 and 3x + y + 4 = 0 is ...… - Vidyadip

MCQ

Angle between the lines $2x - y - 15 = 0$ and $3x + y + 4 = 0$ is .....$^o$

A
${90}$
✓
${45}$
C
${180}$
D
${60}$

✓

Answer

Correct option: B.

${45}$

b
(b)Lines are $2x - y - 15 = 0$ .....(i)
and $3x + y + 4 = 0$ ......(ii)
Here, ${m_1} = 2,\,{m_2} = - \,3$
If angle between them is $\theta $, then
$\tan \theta = \left| {\frac{{{m_1} - {m_2}}}{{1 + {m_1}{m_2}}}} \right|$ $ = \left| {\frac{{2 + 3}}{{1 - 6}}} \right| = \left| {\frac{5}{{ - 5}}} \right|$= 1
$\tan \theta = \tan \frac{\pi }{4}$ ==> $\theta = \frac{\pi }{4} = 45^\circ .$

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