Question

Show that vector area of quadrilateral abcd is 1/2(acbd), where ac and bd are its diagonals

Answer 1

Answer:

To prove the above theorem , let me proceed with an example rather than the normal conventional problem, let us consider a square of length 1 unit, by applying pythagoras theorem we get the length of the diagonals to be √2 The dot product of 2 diagonals will be ac. bd= 2

The area of the quadrilateral = 1²= 1= (ac.bd)÷2

Hence proved.