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JEE Main20249 Apr 2024Morning ShiftMathematicsVector AlgebraActual

Let O A =2 a , O B =6 a +5 b and O C =3 b , where O is the origin. If the area of the parallelogram with adjacent sides OA and OC is 15 sq. units, then the area (in sq. units) of the quadrilateral OABC is equal to :

Options

  1. A32
  2. B40
  3. C38
  4. D35

Correct answer

D. 35

Step-by-step solution

Area of parallelogram having sides aligned & OA & OC =| OA OC |=|2 a 3 b |=15 & 6| a b |=15 & | a b |= 5 2 . .(1) aligned Area of quadrilateral aligned & OABC = 1 2 | d ₁ d ₂ | & = 1 2 | AC OB |= 1 2 |(3 b -2 a ) (6 a +5 b )| & = 1 2 |18 b a -10 a b |=14| a b | & =14 5 2 =35 aligned

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