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AP EAMCET201920 Apr 2019Morning 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 (30^ ), then the value of (|( A B ) C | ) is

Options

  1. A( 2 3 )
  2. B( 3 2 )
  3. C3
  4. D2

Correct answer

B. ( 3 2 )

Step-by-step solution

Since, ( A =2 i + j -2 k ) and ( B = i + j ) so ( aligned & A B = | array ccc i & j & k 2 & 1 & -2 1 & 1 & 0 array |= i (2)- j ( Z )+ k (2-1) & =2 i -2 j + k & |( A B ) C |=| A B || C | 30^ aligned ) [as angle between ( A B ) and ( C =30^ ) (given)] ( aligned & = 4+4+1 | C | ( 1 2 )= 3 2 | C | (i) & | C - A |=2 2 (Given) & | C |^2+| A |^2-2 C A =8 & |C|^2+9-2|C|=8 [as A C =| C |] & (| C |-1)^2=0 | C |=1 aligned ) So, (|( A B ) C |= 3 2 ) [from Eq. (i)] Hence, option (2) is correct.

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