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Question

Find the area of the parallelogram whose diagonals are represented by the vectors 2^i+3^j6^k and 3^i4^j^k.

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Solution

Diagonals of the parallelogram are represented by 2^i+3^j6^k and 3i4jk.
Area of parallelogram =12A×B
(Here, A,B are vectors of diagonals of parallelogram).
Area =12|(2i+3j6k)×(3i4jk)|
=12|27i16j17k|
=12(27)2+(16)2+(17)2
=121274
=12726=7262.

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