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MHT CET20243 May 2024Evening ShiftMathematicsVector AlgebraActual

If a = a ₁ i + a ₂ j + a ₃ k , b = b ₁ i + b ₂ j + b ₃ k and c =c₁ i +c₂ j +c₃ k are non-zero non-coplanar vectors and m is non-zero scalar such that value of m is equal to

Options

  1. A2
  2. B3
  3. C4
  4. D7

Correct answer

B. 3

Step-by-step solution

aligned & [ array lll m a + b & ~m ~b + c & ~m c + a array ]=28 [ array lll a & ~b & c array ] & ( ma + b )[( m ~b + c ) ( m c + a )]=28 [ array lll a & ~b & c array ] & (m a + b ) & [ m ^2( ~b c )+ m ( ~b a )+ m ( c c )+( c a ) ] & =28 [ array lll a & ~b & c array ] aligned aligned & ( ma + b ) [ m ^2( ~b c )+ m ( ~b a )+( c a ) ] & =28 [ array lll a & ~b & c array ] & m a m^2( ~b c )+ m ^2 a ( ~b a )+ ma ( c a ) & + b ~m ^2( ~b c )+ b ~m ( ~b a )+ b ( c a ) & =28 [ array lll a & ~b & c array ] . aligned aligned &

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