Q. 113.7( 30 Votes )

# . Find the angle

Answer :

We know that

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

cos θ = | l_{1}l_{2} + m_{1}m_{2} + n_{1}n_{2} | ……(i)

(i) and

Here, a_{1} = 2, b_{1} = 5, c_{1} = -3 and a_{2} = -1, b_{2} = 8, c_{2} = 4

Now, ……(ii)

Here,

And

So, from (ii), we have

⇒

And

∴ From (i), we have

⇒

⇒

(ii) and

Here, a_{1} = 2, b_{1} = 2, c_{1} = 1 and a_{2} = 4, b_{2} = 1, c_{2} = 8

Here,

And

So, from (ii), we have

⇒

And

∴ From (i), we have

⇒

⇒

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