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Question
Find the angles between the following pair of straight lines:
3x + 4y − 7 = 0 and 4x − 3y + 5 = 0
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Solution
The equations of the lines are
3x + 4y − 7 = 0 ... (1)
4x − 3y + 5 = 0 ... (2)
Let \[m_1 \text { and } m_2\] be the slopes of these lines.
\[m_1 = - \frac{3}{4}, m_2 = \frac{4}{3}\]
\[\because m_1 m_2 = - \frac{3}{4} \times \frac{4}{3}\]
\[ = - 1\]
Hence, the given lines are perpendicular.
Therefore, the angle between them is 90°.
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