Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202314 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The mirror image of P (2,4,-1) in the plane x-y+2 z-2=0 is ( a , b , c ) , then the value of a + b + c is

Options

  1. A4
  2. B5
  3. C7
  4. D9

Correct answer

D. 9

Step-by-step solution

The d.r.s. of the normal to the plane are 1,-1,2 . The equation of line PM is aligned & x-2 1 = y-4 -1 = z +1 2 = ( say ) & x= +2, y=- +4, z =2 -1 & Let M ( +2,- +4,2 -1) aligned array ll & Equation of plane becomes & 1( +2)-1(- +4)+2(2 -1)-2=0 & =1 & M (3,3,1) array Since M is the mid-point of P Q . aligned & 2+ a 2 =3, 4+ b 2 =3, -1+ c 2 =1 & a =4, ~b =2, c =3 & a + b + c =9 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