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MHT CET202311 May 2023Morning 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 6 , then |( a b ) c | is

Options

  1. A3 2
  2. B2 3
  3. C1
  4. D3 4

Correct answer

A. 3 2

Step-by-step solution

aligned & | c - a |^2=2 2 & | c |^2+| a |^2-2( a c )=8 & | c |^2+9-2| c |=8 & (| c |⁻¹ )^2=0 & | c |^2=1 aligned Now, aligned |( a b ) c | & =|( a b )|| c | 6 & =| a b |(1) ( 1 2 ) [ From (i) ] & = 3 2 [ a b =2 i -2 j + k ] aligned

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