Explanation

(a)
Any plane through the given planes is $x + 2y + 3\mathcal{z} - 4 + \lambda\left( 4x + 3y + 2\mathcal{z} + 1 \right) = 0$
It passes through ($0,\ 0,\ 0$). Therefore,
$- 4 + \lambda = 0$
$\therefore\ \lambda = 4$
Therefore, the required plane is $x + 2y + 3\mathcal{z} + 4(4x + 3y + 2\mathcal{z}) = 0$ or $17x + 14y + 11\mathcal{z} = 0$