Explanation

(b)
Let $\overrightarrow{\mathbf{A}} = \widehat{\dot{\mathbf{i}}} - 2\widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}},\ \ \overrightarrow{\mathbf{B}} = - 2\widehat{\dot{\mathbf{i}}} + 3\widehat{\dot{\mathbf{j}}} - \widehat{\mathbf{k}}$
$and\ \overrightarrow{\mathbf{C}} = 4\widehat{\dot{\mathbf{i}}} - 7\widehat{\dot{\mathbf{j}}} + 7\widehat{\mathbf{k}}$
$\therefore\ \ \overrightarrow{\mathbf{AB}} = - 3\widehat{\dot{\mathbf{i}}} + 5\widehat{\dot{\mathbf{j}}} - 4\widehat{\mathbf{k}}$
$and\ \overrightarrow{\mathbf{AC}} = 3\widehat{\dot{\mathbf{i}}} - 5\widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}}$
$\therefore Area\ of\ \mathrm{\Delta}\ ABC = \frac{1}{2}||\overrightarrow{\mathbf{AB}} \times \overrightarrow{\mathbf{AC}}||$
$= \frac{1}{2}\left| \begin{matrix}
\widehat{\dot{\mathbf{i}}} & \widehat{\dot{\mathbf{j}}} & \widehat{\mathbf{k}} \\
- 3 & 5 & - 4 \\
3 & - 5 & 4
\end{matrix} \right| = \frac{1}{2}\left| \begin{matrix}
\widehat{\dot{\mathbf{i}}} & \widehat{\dot{\mathbf{j}}} & \widehat{\mathbf{k}} \\
- 3 & 5 & - 4 \\
0 & 0 & 0
\end{matrix} \right|$
[operating $R_{2} \rightarrow R_{2} + R_{3}\rbrack$
$= \frac{1}{2}\lbrack 0\rbrack = 0$