Diketahui dua buah vektor \(\overrightarrow a = 2 \: \widehat i - 2 \: \widehat j + \: \widehat k\) dan \(\overrightarrow b = 3 \: \widehat i + \: \widehat j + 2 \: \widehat k\).
(A) \(\overrightarrow a \times \overrightarrow b\)
\begin{equation*}
\begin{split}
\overrightarrow a \times \overrightarrow b & = \begin{vmatrix}
\: \widehat i & \: \widehat j & \: \widehat k \\
2 & -2 & 1 \\
3 & 1 & 2 \\
\end{vmatrix} \\\\
\overrightarrow a \times \overrightarrow b & = \: \widehat i \:
\begin{vmatrix}
-2 & 1 \\
1 & 2
\end{vmatrix}
- \: \widehat j \:
\begin{vmatrix}
2 & 1 \\
3 & 2
\end{vmatrix}
+ \: \widehat k \:
\begin{vmatrix}
2 & -2 \\
3 & 1
\end{vmatrix} \\\\
\overrightarrow a \times \overrightarrow b & = \: \widehat i \: (-4 - 1) - \: \widehat j \: (4 - 3) + \: \widehat k \: (2 + 6) \\\\
\overrightarrow a \times \overrightarrow b & = -5 \: \widehat i - \: \widehat j + 8 \: \widehat k
\end{split}
\end{equation*}
(B) \(\overrightarrow b \times \overrightarrow a\)
\begin{equation*}
\begin{split}
\overrightarrow b \times \overrightarrow a & = - \overrightarrow a \times \overrightarrow b \\\\
\overrightarrow b \times \overrightarrow a & = - (-5 \: \widehat i - \: \widehat j + 8 \: \widehat k) \\\\
\overrightarrow b \times \overrightarrow a & = 5 \: \widehat i + \: \widehat j - 8 \: \widehat k
\end{split}
\end{equation*}
