Question

Prove by vector method that the parallelogram on the same base andbbetween the zame parallel are equal in area

Answer 1

Let AB−→−=a⃗  and AD−→−=b⃗ We know that the vector area of paralleogram is the cross product of its adjacent sides.⇒Vector area of parallelogram ABCD=a⃗ ×b⃗   ;(i)Now consider the parallelogram ABB'A'HereLet AB−→−=a⃗  and A'D=ma⃗  because A'D−→− is parallel to AB−→−.Consider triangle ADA'By triangle law of vectorsAA'=ma⃗ +b⃗ Hence:Vector area of parallelogram ABB'A'=a⃗ ×(ma⃗ +b⃗ )=m(a⃗ ×a⃗ )+a⃗ ×b⃗ We know that a⃗ ×a⃗ =0, henceVector area of parallelogram ABB'A'=a⃗ ×b⃗  ;(ii)By (i) and (ii), we get:Vector area of parallelogram ABCD=Vector area of parallelogram ABB'A'

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Answer 2

Answer:

Step-by-step explanation: