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MHT CET202020 Oct 2020Morning ShiftMathematicsVector AlgebraActual

If a , b , c are non - coplanar vectos and ( a + b + c ) ( a b + b c + c a )= k [ a b c ] , then value of k is

Options

  1. A4
  2. B1
  3. C2
  4. D3

Correct answer

D. 3

Step-by-step solution

aligned &( a + b + c ) [( a b )+( b c )+( c a )] =&[ a ( a b )]+[ a ( b c )]+[ a ( c a )]+[ b ( a b )]+[ b ( b c )] &+[ b ( c a )]+[ c ( a b )]+[ c ( b c )]+[ c ( c a )] =& 0+[ a ( b c )]+0+0+0+[ b ( c a )]+[ c ( a b )]+0+0 =& 3[ a ( b c )]=3 [ array lll a & b & c array ] k =3 aligned

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