Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Find the Angles Between the Following Pair of Straight Lines: 3x + Y + 12 = 0 and X + 2y − 1 = 0 - Mathematics

Answer in Brief

Find the angles between the following pair of straight lines:

3x + y + 12 = 0 and x + 2y − 1 = 0

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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 \[ 45^\circ\]

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APPEARS IN

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