Question

ABCD is a parallelogram . AC and BD are its diagonals . show that
(a)AC+BD=2BC
(b)AC-BD=2AB

Answer 1

Answer:

Answer is given above.

Answer 2

By applying the triangle law of vector addition we get,

$AC=AB+BC$ & $BD=BC+CD$

(i)AC+BD=2BC

           $AC+BD=AB+BC+BC+CD$

                            $=-CD+BC+BC+CD [AB=-CD]$

                            $=2BC$

(ii)$AC-BD=2AB$

              $AC-BD=AB+BC-BC-CD$

                               $=AB-CD$       [CD=-AB]

                               $=AB-(-AB)$

                             $=2AB$

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