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MHT CET202619 April 2026Morning ShiftMathematicsVector AlgebraActual

If A( a ) , B( b ) and C( c ) are vertices of ABC . Point D divides segment BC internally in the ratio 2 : 1 . Point E divides segment AD internally in the ratio 1 : 2 , then the position vector of E is ____

Options

  1. A3 a + 4 b + 2 c 9
  2. B6 a + 2 b + c 9
  3. C3 a + 2 b + 4 c 9
  4. D6 a + b + 2 c 9

Correct answer

D. 6 a + b + 2 c 9

Step-by-step solution

Point D divides the segment BC internally in the ratio 2 : 1 . Using the section formula, the position vector of D is given by: d = 2 c + 1 b 2 + 1 = b + 2 c 3 Point E divides the segment AD internally in the ratio 1 : 2 . The position vector of E is given by: e = 1 d + 2 a 1 + 2 = 2 a + d 3 Substituting the value of d into the equation for e : e = 2 a + b + 2 c 3 3 e = 6 a + b + 2 c 3 3 e = 6 a + b + 2 c 9 Answer: 6 a + b + 2 c 9

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