Find the area of the parallelogram whose adjacent sides are given by the vectors `veca=hati-hatj+3hatk and vecb=2hati-7hatj+hatk``

Explanation

The area of the parallelgram whose adjacent sides are `veca and vecb is |veca xx vecb|`
Adjacent sides are given as
`veca=hati-hatj+3hatkand vecb=2hati-7hatk+hatk`
`vecaxxvecb=|{:(hati,hatj,hatk),(1,-1,3),(2,-7,1):}|=hati(-1+21)-hatj(1-6)+hatk(-7+2)=20hati=5hatj-5hatk`
`|vecaxxvecb|=sqrt(20^(2)+5^(2)+(-5)^(2))=sqrt(400+25+25)=15sqrt2`
Hence, the area of the given parllelogram is `15sqrt2` square units.