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AP EAMCET202021 Sep 2020Evening ShiftMathematicsVector AlgebraActual

Let (A B C D E F ) be a regular hexagon with the vertices (A, B, C, D, E, F ) counterclock-wise. Then the vector ( A B + A F + C D + E F ) is equal to

Options

  1. A( DE + FA )
  2. B( CB + ED )
  3. C( BC + FA )
  4. D( BC + DE )

Correct answer

D. ( BC + DE )

Step-by-step solution

In a regular hexagon (A B C D E F ), We know that, ( A B + B C + C D = A D =2 B C ) ( array rrr & A B + C D & = B C (i) Similarly, as & A F & = C D (ii) array ) and as we know that ( array l CD + DE + EF = CF =2 DF CD + EF = DE (iii) array ) from Eqs. (i) and (iii), we get ( aligned & A B + C D + C D + E F = B C + D E & A B + A F + C D + E F = B C + D E aligned ) from Eq. (ii)

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