The diagonals of a parallelogram are expressed as `vecA=5hati05hatj+3hatk` and `hatB=3hatj-2hatj-hatk`.
Calculate the magnitude of area of this parallelogram.

Explanation

When `vecA` and `vecB` are the diagonals of a parallelegram, then its
Area `=(1)/(2)|vecAxxvecB|`
`vecAxxvecB=|{:(hati,hatj,hatk),(5,-4,3),(3,-2,-1):}|=i|{:(-4,3),(-2,-1):}|-j|{:(5,3),(3,-1):}|+k|{:(5,-4),(3,-2):}|`
`=hati{(-4)(-1)-(3)(-2)}-hatj{(5)(-2)-(-4)(3)}=10hati+14hatj+2hatk`
therefore `|vecAxxvacB|=sqrt((10)^(2)+(14)^(2)+(2)^(2))=sqrt(300)`
So area of parallelogram `=(1)/(2)|vecAxxvecB|=(1)/(2)xx10sqrt(3)=5sqrt(3)`