AREA OF PARALLELOGRAM



AREA OF PARALLELOGRAM
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)
Area of Parallelogram

Draw perpendicular CD on side OA.
Consider right angled triangle COD
 sinq = h/OChOC sinq hB sinq
Putting the value of h in equation (1), we get,
D = B sinq AD = AB sinq
OR

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