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AP EAMCET20228 Jul 2022Morning ShiftMathematicsVector AlgebraActual

A , B , C , D are any 4 points and | A B C D + B C A D + C A B D |= (Area of A B C ) then =

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

Given four points A, B, C and D with position vectors a , b , c and d respectively. Now | AB CD + BC AD + CA BD |= Area of ABC . aligned & |( b - a ) ( a - c )+( c - b ) ( d - a )+( a - c ) ( d - b )| & 2 | a b + b c + c a | & 2| a b + b c + c a |= 2 | a b + b c + c a | aligned Compare above equation, gathered 2= 2 =4 gathered

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