Answer
For the rain gauge to collect a maximum amount of water, vector R and vector A should be parallel to each other.
Work Step by Step
Let $\theta$ be the angle between vector R and vector A.
$V = \vert ~R \cdot A ~\vert$
$V = \vert ~R ~\vert ~\vert A ~\vert~cos(\theta)$
V is the volume of rain collected in the rain gauge.
To maximize V, we need to maximize the value of $cos(\theta)$. The value of $cos(\theta)$ has a maximum possible value of 1, when $\theta = 0^{\circ}$.
Therefore, for the rain gauge to collect a maximum amount of water, vector R and vector A should be parallel to each other.
