Volume of Parallelepiped (평행육면체의 부피)



Volume of Parallelepiped
An alternative method defines the vectors @@ \textbf{a} = (a_1, a_2, a_3), \textbf{b} = (b_1, b_2, b_3)@@ and @@\textbf{c} = (c_1, c_2, c_3)@@ to represent three edges that meet at one vertex. The volume of the parallelepiped is equal to the absolute value of the scalar triple product @@ \textbf{a} \cdot ( \textbf{b} \times \textbf{c})@@ and the absolute value of the determinant of a three dimensional matrix built using @@\textbf{a}, \textbf{b}@@ and @@\textbf{c}@@ as rows (or columns) :
@@ V= \begin{vmatrix} det\begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix} \end{vmatrix}@@.