JEE Main202623 January 2026Morning ShiftMathematicsThree Dimensional GeometryActual

Let the direction cosines of two lines satisfy the equations : 4 l+m-n=0 and 2 m n+10 n l+3 l m=0 . Then the cosine of the acute angle between these lines is :

Options

A20 3 38
B10 3 38
C10 7 38
D10 38

Correct answer

B. 10 3 38

Step-by-step solution

From n = 4l + m , substitute in 2mn + 10nl + 3lm = 0 : 40l^2 + 21lm + 2m^2 = 0 . Let t = l/m : 40t^2 + 21t + 2 = 0 . t = -21 11 80 , giving t = -1/8 or t = -2/5 . l/m = -1/8 : direction (l,m,n) = (-1, 8, 4) . l/m = -2/5 : direction (l,m,n) = (-2, 5, -3) . = |2+40-12| 81 38 = 30 9 38 = 10 3 38 .

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