Find the acute angle between the lines $2 x - y + 3 = 0$ and $x - 3 y + 2 = 0$ .

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Solution

Let the slope of the lines $m_{1} = 2$ and $m_{2} = \frac{1}{3}$
And
$t a n θ = | \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} |$

$= ∣ ∣ ∣ ∣ ∣ ∣ \frac{\frac{1}{3} - 2}{1 + \frac{1}{3} .2} ∣ ∣ ∣ ∣ ∣ ∣ = 1$

$θ = 45^{\circ}$

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