Explanation

(b)
The equation of a plane through the line of intersection of the planes $\overrightarrow{r}.\overrightarrow{a} = \lambda\$and$\ \overrightarrow{r}.\overrightarrow{b} = \mu\$is
$(\overrightarrow{r}.\overrightarrow{a} - \lambda) + k\left( \overrightarrow{r}.\overrightarrow{b} - \mu \right) = 0\$or$\ \overrightarrow{r}.\left( \overrightarrow{a} + k\overrightarrow{b} \right) = \lambda + k\mu$ (i)
This passes through the origin, therefore
$\overrightarrow{0}\left( \overrightarrow{a} + k\overrightarrow{b} \right) = \lambda + \mu k\ \Rightarrow k = \frac{- \lambda}{\mu}$
Putting the value of $k$ in (i). we get the equation of the required plane as
$\overrightarrow{r}.\left( \mu\overrightarrow{a} - \lambda\overrightarrow{b} \right) = 0\ \Rightarrow \ \overrightarrow{r}.\left( \lambda\overrightarrow{b} - \mu\overrightarrow{a} \right) = 0$