Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202616 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

The values of p and q so that the line joining the points (7, p, 2) and (q, -2, 5) may be parallel to the line joining the points (2, -3, 5) and (-6, -15, 11) are

Options

  1. Ap = 4, q = -3
  2. Bp = 4, q = 3
  3. Cp = -4, q = 3
  4. Dp = -4, q = -3

Correct answer

B. p = 4, q = 3

Step-by-step solution

The direction ratios of the line joining the points (7, p, 2) and (q, -2, 5) are (q - 7, -2 - p, 5 - 2) = (q - 7, -2 - p, 3) . The direction ratios of the line joining the points (2, -3, 5) and (-6, -15, 11) are (-6 - 2, -15 - (-3), 11 - 5) = (-8, -12, 6) . Since the two lines are parallel, their direction ratios are proportional: q - 7 -8 = -2 - p -12 = 3 6 q - 7 -8 = -2 - p -12 = 1 2 Equating the terms to 1 2 : q - 7 -8 = 1 2 q - 7 = -4 q = 3 -2 - p -12 = 1 2 -2 - p = -6 p = 4 Therefore, p = 4 and q = 3 . Answer:

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 MHT CET PYQs