NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The direction cosines of two lines satisfy 2 l + 2 m - n = 0 and l m + m n + n l = 0 . The angle between these lines is

Options

Aπ 4
Bπ 2
Cπ 6
Dπ 3

Correct answer

B. π 2

Step-by-step solution

Substituting n = 2 l + m in l m + m n + n l = 0 , we get l m + 2 l + m 2 = 0 ⇒ 2 l 2 + 5 l m + 2 m 2 = 0 ⇒ 2 l + m l + 2 m = 0 Hence m = - 2 l ⇒ n = - 2 l or m = - l 2 ⇒ n = l So D.C’s of the lines are ( l , - 2 l , - 2 l ) or l , - l 2 , l Hence, the angle between them is 90 o

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