Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2015MathematicsThree Dimensional Geometry

The cartesian equation of the plane passing through the point (3,-2,-1) and parallel to the vectors b = i -2 j +4 k and c =3 i +2 j -5 k is

Options

  1. A(a) 2 x-17 y-8 z+63=0
  2. B3 x+17 y+8 z-36=0
  3. C2 x+17 y+8 z+36=0
  4. D3 x-16 y+8 z-63=0

Correct answer

C. 2 x+17 y+8 z+36=0

Step-by-step solution

Vector b and c are given as, b = i -2 j +4 k and c=3 i +2 j -5 k Cartesian equation of plane passing through the point (3,-2,-1) aligned & | array ccc x-x₁ & y-y₁ & z-z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ array |=0 & | array ccc x-3 & y+2 & z+1 1 & -2 & 4 3 & 2 & -5 array |=0 & (x-3)(10-8)-(y+2)(-5-12)+(z+1)(2+6)=0 & (x-3)(2)-(y+2)(-17)+(z+1) 8=0 & 2 x-6+17 y+34+8 z+8=0 & 2 x+17 y+8 z+36=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 AP EAMCET PYQs