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Manipal MET2015MathematicsVector Algebra

Let a =2 i + j -2 k and b = i + j . If c is a vector such that a c =| c |,| c - a |=2 2 and the angle between a b and c is 30^ . Then, ( a b ) c is equal to

Options

  1. A2 3
  2. B3 2
  3. C2
  4. D3

Correct answer

B. 3 2

Step-by-step solution

We have, a b = | array ccc i & j & k 2 & 1 & -2 1 & 1 & 0 array |=2 i -2 j + k and | b |= 2^2+2^2+1^2 = 4+4+1 =3 |( a b ) c |=| a b || c | 30^ = 3 2 |c| Given, |c-a|=2 2 array rr & |c-a|^2=8 & |c|^2+|a|^2-2( a c )=8 & |c|^2+9-2| c |=8 & |c|^2-2| c |+1=0 & |c|=1 array Hence, |( a b ) c |= 3 2

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