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MHT CET202615 April 2026Morning ShiftMathematicsVector AlgebraActual

If ABCDEF is a regular hexagon and AB + AC + AD + AE + AF = p AD = q AO , where O is the center of the hexagon, then the values of p and q respectively are

Options

  1. A2, 3
  2. B4, 6
  3. C3, 6
  4. D3, 5

Correct answer

C. 3, 6

Step-by-step solution

Let O be the origin. The position vectors of the vertices A, B, C, D, E, F are a , b , c , d , e , f respectively. Since ABCDEF is a regular hexagon with center O , the position vectors of opposite vertices are negatives of each other. Thus, d = - a , e = - b , and f = - c . The given sum of vectors is: AB + AC + AD + AE + AF = ( b - a ) + ( c - a ) + ( d - a ) + ( e - a ) + ( f - a ) = b + c + d + e + f - 5 a Substituting d = - a , e = - b , and f = - c : = b + c - a - b - c - 5 a = -6 a The vector AO is given by

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