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Find the area of a parallelogram whose...

Find the area of a parallelogram whose diagonals are ` vec a=3 hat i+ hat j-2 hat k and vec b= hat i-3 hat j+4 hat kdot`

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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