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find the area of a parallelogram whose d...

find the area of a parallelogram whose diagonals are `veca=3hati+hatj-2hatk and vecb=hati-3hatj+4hatk`.

Text Solution

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`Delta=1/2|vecaxxvecb|`
`vecaxxvecb=|{:(hati,hatj,hatk),(3,1,-2),(1,-3,4):}|=-2hati-14hatj-10hatk`
`Herce, Delta=1/2|vecaxxvecb|=1/2sqrt(4+196+100)=5sqrt3`
Hence, the area of the given parallelogram is `15sqrt2` square units.
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