AP EAMCET202315 May 2023Evening ShiftMathematicsVector AlgebraActual
If 7 i -4 j +5 k is the position vector of the vertex A of a tetrahedron A B C D and - i +4 j -3 k is the position vector of the centroid of the triangle BCD , then the position vector of the centroid of the tetrahedron A B C D is
Options
- A- i +4 j -3 k
- B- 1 2 i +4 j -3 k
- Ci +2 j - k
- D- i -2 j + k
Correct answer
C. i +2 j - k
Step-by-step solution
aligned & aligned A & =7 i -4 j +5 k C _ B C D & = B + C + D 3 =- i +4 j -3 k aligned & Centroid of tetrahedron A B C D & aligned C _ A B C D & = 1 4 ( A + B + C + D ) & = 1 4 [ A +3 ( B + C + D 3 ) ] & = 1 4 [7 i -4 j +5 k +3(- i +4 j -3 k )] & = i +2 j - k . aligned aligned