Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2002MathematicsThree Dimensional Geometry

The direction ratios of normal to the plane passing through (0,0,1),(0,1,2) and (1,0,3) , are

Options

  1. A(2,1,-1)
  2. B(1,0,1)
  3. C(0,0,-1)
  4. D(1,0,0)

Correct answer

A. (2,1,-1)

Step-by-step solution

Equation of the plane passing through (0,0,1),(0 , 1,2) and (1,0,3) is | array llll x & y & z & 1 0 & 0 & 1 & 1 0 & 1 & 2 & 1 1 & 0 & 3 & 1 array |=0 Applying C₃ C₃-C₄ aligned & | array cccc x & y & z-1 & 1 0 & 0 & 0 & 1 0 & 1 & 1 & 1 1 & 0 & 2 & 1 array |=0 & | array ccc x & y & z-1 0 & 1 & 1 1 & 0 & 2 array |=0 & aligned Applying C₂ C₂-C₃ aligned & | array ccc x & y-z+1 & z-1 0 & 0 & 1 1 & -2 & 2 array |=0 & - | array cc x & y-z+1 1 & -2 array |=0 & -[-2 x-(y-z+1)]=0 & 2 x+y-z+1=0 & aligned aligned & -[-2 x-(y-z+

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