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

Let `vec(A)=2hat(i)+3hat(j)+hat(k)` and `vec(B)=hat(i)-hat(j)+2hat(k)`
Unit vector perpendicular to both `vec(A)` and `vec(B)` is `hat(n)=(vec(A)xxvec(B))/(|vec(A)xxvec(B)|)`
`vec(A)xxvec(B)=|(hat(i),hat(j),hatk),(2,3,1),(1,-1,2)|=hat(i)(6+1)-hat(j)(4-1)+hat(k)(-2-3)=7hat(i)-3hat(j)-5hat(k)`
`:.|vec(A)xxvec(B)|=sqrt(7^(2)+(-3)^(2)+(-5)^(2))=sqrt(83)` unit
`:. hat(n)=1/sqrt(83)(7hat(i)-3hat(j)-5k)`