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JEE Main20246 Apr 2024Evening ShiftMathematicsVector AlgebraActual

Let a =6 i + j - k and b = i + j . If c is a is vector such that | c | 6, a c =6| c |,| c - a |=2 2 and the angle between a b and c is 60^ , then |( a b ) c | is equal to:

Options

  1. A9 2 (6- 6 )
  2. B3 2 6
  3. C9 2 (6+ 6 )
  4. D3 2 3

Correct answer

C. 9 2 (6+ 6 )

Step-by-step solution

aligned & |( a b c )|=| a b || c | 3 2 & | c - a |=2 2 & | c |^2+| a |^2-2 c a =8 & | z |^2+38-12| z |=8 & | z |^2-12| z |+30=0 & | z |= 12 144-120 2 & = 12 2 6 2 aligned aligned & |z|=6+ 6 & a b = | array ccc & j & k 6 & 1 & -1 1 & 1 & 0 array | & - j +5 k & | a b |= 27 & |( a b ) z |= 27 (6+ 6 ) 3 2 & 9 2 (6+ 6 ) aligned

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