# . 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

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