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AP EAMCET202018 Sep 2020Evening ShiftMathematicsVector AlgebraActual

In a regular hexagon (A B C D E F ), ( A D + E B + F C =( -8) A B ). Then ( = )

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

B. 4

Step-by-step solution

Since, ( A D | B C ) and ( A D =2 B C ) ( gathered E B | F A and E B =2 F A F C | A B and F C =2 A B gathered ) ( A D + E B =2( B C + F A )=2( A O + F A ) ) ...(i) In ( AOF ), ( aligned F A + A O + O F & =0 F A + A O & =- O F (ii) aligned ) Put, Eqs. (ii) in (i) ( aligned & A D + E B =2(- O F )=2 F O & A D + E B =2 A B aligned ) Now consider, ( array rlrl A D + E B + F C & =2 A B +2 A B [ F C =2 A B ] (3 -8) A B & =4 A B [ given ] 3 -8 & =4 3 & =12 & & =4 & array ) Hence, option (b) is correct.

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