Dua buah vektor \(\overrightarrow p = \left( \begin{matrix} a \\ b \\ c \\ \end{matrix} \right)\) dan \(\overrightarrow q = \left( \begin{matrix} d \\ e \\ f \\ \end{matrix} \right)\)
\begin{equation*}
\begin{split}
\overrightarrow p \times \overrightarrow q & = \begin{vmatrix}
i & j & k \\
a & b & c \\
d & e & f \\
\end{vmatrix}
= i \:
\begin{vmatrix}
b & c \\
e & f
\end{vmatrix}
- j \:
\begin{vmatrix}
a & c \\
d & f
\end{vmatrix}
+ k \:
\begin{vmatrix}
a & b \\
d & e
\end{vmatrix}
\end{split}
\end{equation*}
\( \overrightarrow q \times \overrightarrow p = - \overrightarrow p \times \overrightarrow q\)
\(| \: \overrightarrow p \times \overrightarrow q \:| = | \: \overrightarrow p \: | \:.\: |\: \overrightarrow q\: | \:.\: \sin \theta \)
Luas Jajaran genjang yang dibentuk oleh vektor \(\overrightarrow p\) dan vektor \(\overrightarrow q\)
\(L = | \: \overrightarrow p \times \overrightarrow q \:|\)
Luas segitiga yang dibentuk oleh vektor \(\overrightarrow p\) dan vektor \(\overrightarrow q\)
\(L = \frac 12 \: | \: \overrightarrow p \times \overrightarrow q \: |\)
MENENTUKAN DETERMINAN MATRIKS
Determinan matriks 2 × 2
\begin{equation*} \begin{split} \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc \end{split} \end{equation*}
Determinan matriks 3 × 3
\begin{equation*} \begin{split} \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{vmatrix} = & = a \: \begin{vmatrix} e & f \\ h & i \end{vmatrix} - b \: \begin{vmatrix} d & f \\ g & i \end{vmatrix} + c \: \begin{vmatrix} d & e \\ g & h \end{vmatrix} \end{split} \end{equation*}