. Find the angle between the following pair of lines:

We know that

If and are the equations of two lines, then the acute angle between the two lines is given by

cos θ = | l₁l₂ + m₁m₂ + n₁n₂ | ……(i)

(i) and

Here, a₁ = 2, b₁ = 5, c₁ = -3 and a₂ = -1, b₂ = 8, c₂ = 4

Now, ……(ii)

Here,

And

So, from (ii), we have

⇒

And

∴ From (i), we have

⇒

⇒

(ii) and

Here, a₁ = 2, b₁ = 2, c₁ = 1 and a₂ = 4, b₂ = 1, c₂ = 8

Here,

And

So, from (ii), we have

⇒

And

∴ From (i), we have

⇒

⇒