Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2024MathematicsThree Dimensional GeometryActual

The angle between the lines whose direction cosines are given by the equations 3 l+m+5 n=0,6 ~nm -2 n l+5 l m =0 is

Options

  1. A⁻¹ ( 1 6 )
  2. B⁻¹ (- 1 6 )
  3. C⁻¹ ( 2 3 )
  4. D⁻¹ (- 5 6 )

Correct answer

B. ⁻¹ (- 1 6 )

Step-by-step solution

The given equations are 3 l+m+5 n=0 ...(i) and 6 mn -2 n l+5 l m =0 ...(ii) From (i), we have m=-3 l-5 n . Putting m =-3 l-5 n in (ii), we get 6(-3 l-5 n) n-2 n l+5 l(-3 l-5 n)=0 (n+l)(2 n+l)=0 either l=- n or l=-2 n . If l=-n , then putting l=-n in (i), we obtain m=-2 n . If l=-2 n , then putting l=-2 n in (i), we obtain m = n . Thus, the direction ratios of two lines are - n ,-2 n , n and -2 n , n , n i.e., 1,2,-1 and -2,1,1 . Hence, the direction cosines are 1 6 , 2 6 , -1 6 or -2 6 , 1 6 , 1 6 . The angle betwe

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The magnitude of projection of line joining (3,4 , 5) and (4,6,3) on the line joining (-1,2,4) and (1,0,5) is 2024Let the acute angle bisector of the two planes x-2 y-2 z+1=0 and 2 x-3 y-6 z+1=0 be the plane P . Then which of the following points lies on P? 2024Let the foot of perpendicular from a point P (1,2,-1) to the straight line L : x 1 = y 0 = z -1 be N . Let a line be drawn from P parallel to the plane x+y+2 z=0 which meets L at p 2024If the co-ordinates of the point in which the line joining the points (3,5,-7) and (-2,1,8) is intersected by the plane y z is [ a , 13 ~b , c ] , then (a+b-c)= 2023If the straight lines x-1 k = y-2 2 = z-3 3 and x-2 3 = y-3 k = z-1 2 intersect at a point, then the integer k is equal to 2023The shortest distance between the lines x = y +2=6 z-6 and x+1=2 y=-12 z is 2023The ratio in which the YZ-plane divide the line segment formed by joining the points (-2,4,7) and (3,-5,8) is 2: m . The value of m is 2023The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar if 2023 Full Three Dimensional Geometry list All BITSAT PYQs