Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.4 Trigonometric Functions - Exercises - Page 31: 65

Answer

$$ m_1m_2=-1 \Rightarrow m_1=\frac{-1}{m_2}$$

Work Step by Step

If the lines are perpendicular, then the angle between them is $\theta=\pi / 2 $ \begin{align*} \cot (\pi / 2)&=\frac{1+m_{1} m_{2}}{m_{1}-m_{2}} \\ 0&=\frac{1+m_{1} m_{2}}{m_{1}-m_{2}} \end{align*} Then $$ m_1m_2=-1 \Rightarrow m_1=\frac{-1}{m_2}$$
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