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MHT CET20249 May 2024Morning ShiftMathematicsVector AlgebraActual

If a , b and c are three non-coplanar vectors, then ( a + b + c ) [( a + b ) ( a + c )] equals

Options

  1. A0
  2. B[ a b c ]
  3. C2[ a b c ]
  4. D-[ a b c ]

Correct answer

D. -[ a b c ]

Step-by-step solution

aligned & [ a + b + c ] [( a + b ) ( a + c )] & =( a + b ) [( a + b ) ( a + c )]+ c [( a + b ) ( a + c )] & =0+[ c a + b a + c ] & =[ c a a + c ]+[ c b a + c ] & =[ c a a ]+[ c a c ]+[ c b a ]+[ c b c ] & =0+0+[ c b a ]+0 & =-[ a b c ] aligned

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