Answer:
By finding the (absolute) value of the Determinant of the matrix of both vectors.
Step-by-step explanation:
1) An area of a parallelogram in Euclidean Geometry is:
[tex]A=b*h[/tex]
2) Similarly, in 3D (with vectors) this area is the magnitude of the cross product of a pair of vectors:
[tex]A=\left \| \vec{u}*\vec{v} \right \|[/tex]
3) But when we want to find the area of a parallelogram spanned by a pair of (column) vectors, we have to find the Determinant of the matrix of both.
E.g.
[tex]\vec{v}=\left \langle v_{1},v_{2} \right \rangle \:\vec{u}=\left \langle u_{1},u_{2} \right \rangle\\\begin{pmatrix} v_{1}&v_{2} \\ u_{1}& u_{2}\end{pmatrix}\\ \begin{vmatrix} v_{1}&v_{2} \\ u_{1}& u_{2}\end{vmatrix} detP=v_{1}u_{2}-u_{1}v_{2}=a \: \:(signed \:area)\\detP=v_{1}u_{2}-u_{1}v_{2}=|a|(unsigned \:area)[/tex]
