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AP EAMCET202124 Aug 2021Morning ShiftMathematicsVector AlgebraActual

Let a , b and c be non-zero vectors such that ( a b ) c = 1 3 | b | c | a . If is the acute angle between the vectors b and c , then is equal to

Options

  1. A1 3
  2. B2 3
  3. C2 3
  4. D2 2 3

Correct answer

D. 2 2 3

Step-by-step solution

aligned & Given, ( a b ) c = 1 3 | b | c | a & - c ( a b ) = 1 3 | b | c | a [ a b =- b a ] & - ( c b ) a -( c a ) b = 1 3 | b | c | a & -( b c ) a +( c a ) b = 1 3 | b | c | a aligned By comparing - b c = 1 3 | b || c | and c a =0 aligned -| b || c | & = 1 3 | b || c | & =- 1 3 & = 1- ^2 & = 1- 1 9 & = 2 2 3 aligned

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