Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

If the direction ratio of two lines are given by 3 l m-4 l n+m n=0 and l+2 m+3 n=0 , then the angle between the lines, is :

Options

  1. A6
  2. B4
  3. C6
  4. D2

Correct answer

D. 2

Step-by-step solution

We have, 3 l m-4 l n+m n=0 (i) and l+2 m+3 n=0 (ii) From Eq. (ii), l=-(2 m+3 n) Using in Eq. (i), we get -3(2 m+3 n) m+4(2 m+3 n) n+m n=0 -6 m^2-9 m n+8 m n+12 n^2+m n=0 -6 m^2+12 n^2=0 Now, m^2=2 n^2 m= 2 n Now, m= 2 n l=-(2 2 n+3 n)=-(2 2 +3) n l: m: n=-(3+2 2 ) n: 2 n: n=-(3+2 2 ): 2 : 1 Also, m=- 2 n l=-(-2 2 +3) nl: m: n=-(3-2 2 ) n:- 2 n: n=-(3-2 2 ):- 2 : 1 If is the angle between the lines, then = l₁ l₂+m₁ m₂+n₁ n₂ l₁^2+m₁^2+n₁^2 l₂^2+m₂^2+n₂^2 = (3+2 2 )(3-2 2 )+( 2 )(- 2 )+1.1 (3+2 2 )^2+( 2 )^2+1^2 (3-2

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

Let P be the plane such that it contains the straight line x-1 2 = y-3 3 = z+2 1 and is perpendicular to the plane x + 2y + 3z = 4 . Let P₁ be the plane which passes through the po 2026Let L be the straight line joining the points P(1, 2, -1) and Q(2, 3, 1) . Let S be the foot of the perpendicular drawn from the point R(4, -1, 5) to the line L . Another line pass 2026Let the foot of perpendicular from the point ( , 2, 3) on the line x-4 1 = y-9 2 = z-5 1 be the point (1, , 2) . Then the distance between the lines x-1 2 = y-2 3 = z+4 6 and x- 2 2026Let a line L₁ pass through the origin and be perpendicular to the lines L₂: r = (3+t) i + (2t-1) j + (2t+4) k and L₃: r = (3+2s) i + (3+2s) j + (2+s) k , t, s R . If (a, b, c) , a 2026The shortest distance between the lines x-4 1 = y-3 2 = z-2 -3 and x+2 2 = y-6 4 = z-5 -5 is : 2026Let the image of the point P(0, -5, 0) in the line x-1 2 = y 1 = z+1 -2 be the point R and the image of the point Q (0, -1 2 , 0 ) in the line x-1 -1 = y+9 4 = z+1 1 be the point S 2026Let the image of the point P(1, 6, a) in the line L: x 1 = y-1 2 = z-a+1 b , b > 0 , be ( a 3 , 0, a+c ) . If S( , , ) , > 0 , is the point on L such that the distance of S from th 2026Let a line L be perpendicular to both the lines L₁: x+1 3 = y+3 5 = z+5 7 and L₂: x-2 1 = y-4 4 = z-6 7 . If is the acute angle between the lines L and L₃: x - 8 7 2 = y - 4 7 1 = 2026 Full Three Dimensional Geometry list All 99 Percentile Qs Bank for JEE Main PYQs