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JEE Main2013MathematicsVector AlgebraActual

Let a =2 i + j -2 k , 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 | equals:

Options

  1. A1 2
  2. B3 3 2
  3. C3
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

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

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