Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20242 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be the image of the point (3,1,7) with respect to the plane x-y+z=3 . Then the equation of the plane passing through P and containing the straight line x 1 = y 2 = z 1 is

Options

  1. A-4 y-x+7 z =0
  2. Bx-4 y-7 z=0
  3. Cx-4 y+7 z=0
  4. Dx+4 y+7 z=0

Correct answer

C. x-4 y+7 z=0

Step-by-step solution

The d.r.s. of the normal to the plane are 1,-1,1 The equation of line QM is aligned & x-3 1 = y-1 -1 = z-7 1 = ( say ) & x= +3, y=- +1, z= +7 aligned Let M ( +3,- +1, +7) Equation of plane becomes aligned & 1( +3)-1(- +1)+1( +7)=3 & 3 +6=0 =-2 & M (1,3,5) aligned Since M is the midpoint of PQ . 3+ a 2 =1, 1+ b 2 =3, 7+ c 2 =5 a=-1, b=5, c=3 Equation of the plane passing through P and containing the given line is aligned & | array ccc x+1 & y-5 & z-3 1 & -5 & -3 1 & 2 & 1 array |=0 & x-4 y+7 z=0 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