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MHT CET20249 May 2024Morning ShiftMathematicsVector AlgebraActual

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 60^ , then the value of |( a b ) c | is

Options

  1. A3 2
  2. B3 3 2
  3. C5 3 2
  4. D3 4

Correct answer

B. 3 3 2

Step-by-step solution

a b = | array ccc i & j & k 2 & 1 & -2 1 & 1 & 0 array |=2 i -2 j + k aligned & | a b |:= 4+4+1 =3 ...(i) & | c - a |=2 2 & |( c - a )^2 |=8 aligned aligned & | c |^2+| a |^2-2 c a =8 & | c |^2+9-2| c |=8 & | c |^2-2| c |+1=0 & (| c |-1)^2=0 & | c |=1 ...(ii) aligned [ a c =| c |] Now, |( a b ) c |=| a b | | c | 60^ aligned & =(3)(1) ( 3 2 ) & = 3 3 2 aligned ...[From (i) and (ii)]

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