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MHT CET202410 May 2024Morning ShiftMathematicsVector AlgebraActual

Let A , B , C be vectors of lengths 3 units, 4 units, 5 units respectively. let A be perpendicular to B + C , B be perpendicular to C + A and C be perpendicular to A + B , then the length of vector A + B + C is

Options

  1. A2 5
  2. B30
  3. C45
  4. D5 2

Correct answer

D. 5 2

Step-by-step solution

aligned & | a |=3,| ~b |=4 and | c |=5 & a ( ~b + c )=0, ~b ( c + a )=0 and c ( a + b )=0 & 2( a ~b + b c + c a )=0 aligned Now, aligned & | a + b + c |^2=| a |^2+| b |^2+| c |^2+2( a ~b + b c + c a ) & | a + b + c |^2=9+16+25+0 [ From ( i ) & | a + b + c |^2=50 & | a + b + c |=5 2 aligned

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