Question

find the angle between the line 2x-y+3=0 and x+y-7=0​

Answer 1

Step-by-step explanation:

The given lines are

$2x - y + 3 = 0 \\ x + y - 7 = 0$

Here,

$m_{1} = 2 \: \: and \: \: m _{2} = - 1$

So,

$\tan( \theta) = \bigg | \frac{m _{2} - m _{1} }{1 + m _{2}m _{1} } \bigg|$

$\implies \tan( \theta) = \bigg | \frac{ - 1 - 2 }{1 + (- 1)(2)} \bigg|$

$\implies \tan( \theta) = \bigg | \frac{ - 3}{1 - 2} \bigg|$

$\implies \tan( \theta) = \bigg | \frac{ - 3}{ - 1} \bigg|$

$\implies \tan( \theta) = 3$

$\implies \theta = \tan^{ - 1} (3)$

So, the angle between the given lines is $\rm\bold{tan^{-1}(3)}$