Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Angles Between the Following Pair of Straight Lines: 3x + Y + 12 = 0 and X + 2y − 1 = 0 - Mathematics

Find the angles between the following pair of straight lines:

3x + y + 12 = 0 and x + 2y − 1 = 0

#### Solution

The equations of the lines are
3x + y + 12 = 0           ... (1)
x + 2y − 1 = 0             ... (2)
Let

$m_1 \text { and } m_2$ be the slopes of these lines.

$m_1 = - 3, m_2 = - \frac{1}{2}$

Let$\theta$ be the angle between the lines.
Then,

$\tan\theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|$

$= \left| \frac{- 3 + \frac{1}{2}}{1 + \frac{3}{2}} \right|$

$= 1$

$\Rightarrow \theta = \frac{\pi}{4}\text { or }45^\circ$

Hence, the acute angle between the lines is $45^\circ$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.13 | Q 1.1 | Page 99