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P and Q are the middle points of diagonals Acme and BD respectively of the quadrilateral.then prove that AB vector+AD vector+CB vector+CD vector=4PQ vector

P and Q are the middle points of diagonals Acme and BD respectively of the quadrilateral.then prove that 
AB vector+AD vector+CB vector+CD vector=4PQ vector 

Grade:12th pass

1 Answers

Arun
25758 Points
3 years ago
Dear student
 
assume position vector of A ,B, C amd D as a , b , c and d
then P = (a + c)/2
and Q = (b+ d)/2
 
then AB+ AD+ CB + CD = b- a + d – a + b- c + d – c = 2(d+ b) – 2 (a + c) = 4 PQ
 

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