Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20244 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane, passing through the point (-1,2,-3) and parallel to the lines. x-1 3 = y-2 2 = z -4 and x 2 = y-1 -3 = z-2 2 , is

Options

  1. A8 x-14 y-13 z-3=0
  2. B8 x-14 y+13 z+75=0
  3. C8 x+14 y+13 z+19=0
  4. D8 x+14 y-13 z-59=0

Correct answer

C. 8 x+14 y+13 z+19=0

Step-by-step solution

Let (x₁, y₁, z₁ )=(-1,2,-3)a₁, b₁, c₁=3,2,-4 and a₂, b₂, c₂=2,-3,2 The equation of required plane is aligned & | array ccc x-x₁ & y-y₁ & z-z₁ a ₁ & ~b ₁ & c ₁ a ₂ & ~b ₂ & c ₂ array |=0 & | array ccc x+1 & y-2 & z +3 3 & 2 & -4 2 & -3 & 2 array |=0 aligned aligned & (x+1)(-8)-(y-2)(14)+(z+3)(-13)=0 & -8 x-8-14 y+28-13 z-39=0 & -8 x-14 y-13 z-19=0 & 8 x+14 y+13 z+19=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