Mathematics Part-II

Book: Mathematics Part-II

Chapter: 11. Three Dimensional Geometry

Subject: Maths - Class 12th

Q. No. 11 of Exercise 11.2

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11

. 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




11

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