Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202312 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If the line 1-x 3 = 7 y-14 2 p = z-3 2 and 7-7 x 3 p = y-5 1 = 6-z 5 are at right angles, then p=

Options

  1. A70 11
  2. B11 70
  3. C-70 11
  4. D-11 70

Correct answer

A. 70 11

Step-by-step solution

Given lines can be written as x-1 -3 = y-2 2 p 7 = z-3 2 and x-1 3 p = y-5 1 = z-6 -5 As these lines are at right angles, we get aligned & -(-3) (- 3 p 7 )+ ( 2 p 7 )(1)+(2)(-5)=0 & 9 p 7 + 2 p 7 -10=0 & 11 p 7 =10 p= 70 11 aligned

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