Explanation

(c)
For an abtuse angle
$\left( cx\widehat{\dot{\mathbf{i}}} - 6\widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}} \right) \bullet \left( x\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + 2cx\widehat{\mathbf{k}} \right) < 0$
$\Longrightarrow \ {cx}^{2} - 12 + 6cx < 0$
$\Longrightarrow cx^{2} + 6cx - 12 < 0$
$\therefore(6c)^{2} - 4c( - 12) < 0\ \ \ \ \lbrack\because f(x) < 0 \Longrightarrow D < 0\rbrack$
$\Longrightarrow 36c\ \left( c + \frac{4}{3} \right) < 0$
$\Longrightarrow - \frac{4}{3} < c < 0$