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Area of a parallelogram

Suppose two vectors $ {\bf v } $ and $ {\bf u}$ in two dimensional space $R^2$ are given which do not lie on the same line. These two vectors form two sides of a parallelogram.

It can be shown that the area of this parallelogram ( which is the product of base and altitude ) is equal to the length of the cross product of these two vectors. So the area of this parallelogram is the absolute value of the determinant of $A=\left[ \begin{array}{rr}
u_1 & u_2\\
v_1 & v_2\\
\end {array}
\right]
$.

\includegraphics[width=4in]{parallelogram.eps}



Subsections

Ali A. Daddel 2000-09-15