The angle between the lines 2x - y + 3 = 0 and x + 2y + 3 = 0 is

Question

The angle between the lines $2 x - y + 3 = 0$ and $x + 2 y + 3 = 0$ is

Smart Achievers · Accepted Answer

(1)

$Given equations of lines are$

$2 x - y + 3 = 0;$ $m_{1} = slope = 2$

$x + 2 y + 3 = 0;$ $m_{2} = slope = \frac{- 1}{2}$

So, $\tan θ =$ $| \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} |$ $=$ $| \frac{2 + \frac{1}{2}}{1 - 1} |$ $= \frac{5}{2 \times 0} = \frac{5}{0} = \infty$

$\Rightarrow$ $\tan θ = \tan \frac{π}{2} \Rightarrow θ = \frac{π}{2}$

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