Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202310 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Two lines x-3 1 = y+1 3 = z-6 -1 and x+5 7 = y-2 -6 = z-3 4 intersect at the point R . Then reflection of R in the x y -plane has co-ordinates

Options

  1. A(2,-4,-7)
  2. B(2,-4,7)
  3. C(-2,4,7)
  4. D(2,4,7)

Correct answer

A. (2,-4,-7)

Step-by-step solution

Let x-3 1 = y+1 3 = z-6 -1 = x=3+ , y=3 -1, z =- +6 Let x+5 7 = y-2 -6 = z-3 4 = x=7 -5, y=-6 +2, z =4 +3 Both the given lines intersect each other. aligned & So, +3=7 -5 & 7 - =8...(i) aligned Also, 3 -1=-6 +2 6 +3 =3 ...(ii) From (i) and (ii), we get aligned & =1, =-1 & i.e., x=2, y=-4, z =7 aligned Co-ordinates of the intersection of the given lines are R (2,-4,7) Hence, reflection of R in the x y -plane is (2,-4,-7) .

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