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MHT CET202016 Oct 2020Morning ShiftMathematicsVector AlgebraActual

In a quadrilateral A B C D, M and N are the mid-points of the sides A B and C D respectively. If A D + B C =t M N , then t=

Options

  1. A4
  2. B2
  3. C1 2
  4. D3 2

Correct answer

B. 2

Step-by-step solution

( C ) Let a , b , c , d , m , n be the position vectors of A, B, C , D , M , N respectively. M and N are the midpoints of AB and CD respectively. m = a + b 2 , and n = c + d 2 a + b =2 m and c + d =2 n We have AD + BC = t ( MN )( d - a )+( c - b )=t( n - m ) d - a + c - b = t ( n - m )( d + c )-( a + b )= t ( n - m )2 n -2 m =t( n - m ) t=2

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