Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201726 Apr 2017Morning ShiftMathematicsThree Dimensional GeometryActual

If the points having the position vectors 3 i -2 j - k , 2 i +3 j -4 k ,- i + j +2 k and 4 i +5 j + k are coplanar, then =

Options

  1. A46 17
  2. B8
  3. C-8
  4. D146 17

Correct answer

A. 46 17

Step-by-step solution

Let A, B, C and D are the position vectors of four points given as aligned & A(3 i -2 j - k ), B(2 i +3 j -4 k ), C(- i + j +2 k ) & and D(4 i +5 j + k ) aligned Here, aligned & AB =- i +5 j -3 k & BC =-3 i -2 j +6 k aligned and C D=5 i +4 j +( -2) k As given that, these points are coplanar, therefore [ AB BC CD ]=0 aligned & | array ccc -1 & 5 & -3 -3 & -2 & 6 5 & 4 & -2 array |=0 & -1(-2 +4-24)-5(-3( -2)-30) & -3(-12+10)=0 & 17 +20+20+15( -2)+150+36-30=0 & 17 +146=0 =- 146 17 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