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Let \( A \) and \( B \) be two points on a parabola \( y^{2}=x \) with vertex \( V \) such that \( V A \) is perpendicular to \( V B \) and \( \theta \) is the angle between the chord \( V A \) and the axis of the parabola. The value of \( \frac{|V A|}{|V B|} \) is :
\( \mathrm{P} \)
(a) \( \tan \theta \)
(b) \( \tan ^{3} \theta \)
(c) \( \cot ^{2} \theta \)
(d) \( \cot ^{3} \theta \)
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