Question

Find the angle between the lines x+2y+13=0 and 2x-y+7=0 is

Answer 1

$\textbf{Given:}$

$\textsf{Lines are}$

$\mathsf{x+2y+13=0\;and\;2x-y+7=0}$

$\textbf{To find:}$

$\textsf{The angle between the given lines}$

$\textbf{Solution:}$

$\mathsf{Slope\;of\;x+2y+13=0\;is\;m_1=\dfrac{-1}{2}}$

$\mathsf{Slope\;of\;2x-y+7=0\;is\;m_2=\dfrac{-2}{-1}=2}$

$\mathsf{Now,}$

$\mathsf{m_1{\times}m_2}$

$\mathsf{=\dfrac{-1}{2}{\times}2}$

$\mathsf{=-1}$

$\implies\textsf{Product of slope is -1}$

$\therefore\textsf{The given two lines are perpendicular}$

$\mathsf{Hence,\;angle\;between\;the\;lines\;is\;90^\circ}$

$\textbf{Find more:}$

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