If two sides of a parallelogram are represented by two vectors A and B, then the magnitude of their cross product will be equal to the area of parallelogram i.e.

**Proof**

Consider a parallelogram OABC whose two sides are represented by two vectors A and B as shown. The area of parallelogram OABC is equal to:

D = hA—————-(1)

Draw perpendicular CD on side OA.

Consider right angled triangle COD

sinq = h/OCh= OC sinq h= B sinq

Putting the value of h in equation (1), we get,

D = B sinq AD = AB sinq

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