Q. 113.8( 22 Votes )

. Find the angle between the following pair of lines:


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 = | 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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