Find the angles between each of the following pairs of straight line: `3x+y+12=0\ a n d\ x+2y-1=0`

Explanation

Given: The equations of the lines are `3x + y + 12 = 0 … (1)`

` x + 2y − 1 = 0 … (2) `

Let m1 and m2 be the slopes of these lines. `m1 = -3, m2 = -1/2 `

Let thetabe the angle between the lines.

Then, by using the formula tan `theta= [(m1 – m2) / (1 + m1m2)] `

`= [(-3 + 1/2) / (1 + 3/2)] = 1 `

So, `theta= pi/4 or 45^o `

∴ The acute angle between the lines is 45°