Find the acute angle between the lines 2x - y + 3 = 0 and x + y +… - Vidyadip

Question

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

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Answer

Slpoe of line 2x - y + 3 = 0 is $\frac{-2}{-1}=\frac{-(\text{coefficient of x})}{(\text{coefficient of y})}=2$
$\therefore\text{m}_1=2 \ ...(\text{i})$
Slpoe of line x + y + 2 = 0 is $\frac{-1}{1}=\frac{-(\text{coefficient of x})}{(\text{coefficient of y})}$
$\therefore\text{m}_2=-1 \ ...(\text{ii})$
Acute angle between lines
$\theta=\tan^{-1}=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$
$=\tan^{-1}=\Big|\frac{2-(-1)}{1-(2)(-1)}\Big|$
$=\tan^{-1}=\Big|\frac{3}{1-2}\Big|=\tan^{-1}=\Big|\frac{3}{1}\Big|=\tan^{-1}|3|$

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