Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2025MathematicsThree Dimensional GeometryActual

The equation of a line passing through origin with direction angles 2 3 , 4 , 3 is

Options

  1. Ax= y 2 =z
  2. Bx -1 = y - 2 =z
  3. Cx= y - 2 =z
  4. Dx= y - 2 =-z

Correct answer

D. x= y - 2 =-z

Step-by-step solution

The direction angles of the line are given as = 2 3 , = 4 , and = 3 . The direction cosines of the line are l = , m = , and n = . Calculating these values: l = ( 2 3 ) = - 1 2 m = ( 4 ) = 1 2 n = ( 3 ) = 1 2 The equation of a line passing through the origin (0, 0, 0) with direction cosines (l, m, n) is given by x l = y m = z n . Substituting the values: x -1/2 = y 1/ 2 = z 1/2 Multiplying the denominators by 2 : x -1 = y 2 = z 1 This can be rewritten as: -x = y 2 = z Multiplying by -1 : x = y - 2 = -z Answer: x= y

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The circum radius of the triangle formed by the points (2,-1,1),(1,-3,-5) and (3,-4,-4) is 2025Let A (2,3,5), B (-1,3,2), C ( , 5, ) be the vertices of ABC . If the median through the vertex A is equally inclined to the coordinate axes, then 2025Equation of the plane passing through the origin and perpendicular to the planes x+2 y-z=1 and 3 x-4 y+z=5 is 2025If the line joining the points i +2 j and j -2 k intersects the plane passing through the points 2 i - j , 2 j +3 k and k -2 i at r , then r ( i + j + k )= 2025The vector equation of a plane passing through the line of intersection of the planes r ( i -2 k )=3, r (2 j + k )=5 and the point i +2 j +3 k is 2025The points A (-1,2,3), B (2,-3,1), C (3,1,-2) 2025The direction cosines of the line making angles 4 , 3 and (0 < < 2 ) respectively with X , Y and Z axes are 2025If the equation of the plane passing through the point (3,2,5) and perpendicular to the planes 2 x-3 y+5 z=7 and 5 x+2 y-3 z=11 is x+b y+c z+d=0 , then 2 b+3 c+d= 2025 Full Three Dimensional Geometry list All COMEDK PYQs