Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202410 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The vector equation of the plane passing through the point A (1,2,-1) and parallel to the vectors 2 i + j - k and i - j +3 k is

Options

  1. Ar (2 i +7 j +3 k )=-9
  2. Br ( i +2 j +2 k )=9
  3. Cr (3 i +2 j -2 k )=9
  4. Dr (2 i -7 j -3 k )=-9

Correct answer

D. r (2 i -7 j -3 k )=-9

Step-by-step solution

Let (x₁, y₁, z₁ )=(1,2,-1) , a ₁, ~b ₁, c ₁=2,1,-1 and : a ₂, ~b ₂, c ₂=1,-1,3 the equation of required plane is aligned & | array ccc x-x₁ & y-y₁ & z-z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ array |=0 & | array ccc x-1 & y-2 & z+1 2 & 1 & -1 1 & -1 & 3 array |=0 & 2 x-2-7 y+14-3 z-3=0 & 2 x-7 y-3 z+9=0 & r (2 i -7 j -3 k )=-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