Answer
(a)$ |\textbf R| \approx 2.2 \text{ in}$ of rain fell
$| \textbf A| \approx 1.1 \text{ in}^2$ (area of the opening of the rain gauge)
(b) $V =1.5\text{ in}^3$ (the volume of rain)
Work Step by Step
$ \textbf R = \dot{i} -2 \dot{j} $
$ \textbf A = 0.5 \dot{i} + \dot{j} $
(a) To find $|R|$ and $| A |$ to the nearest tenth. Interpret the results
$ |\textbf R| = |\dot{i} -2 \dot{j}|=\sqrt { 1^2+(-2)^2}=\sqrt 5\approx 2.2 $ inches of rain fell.
|$ \textbf A| =| 0.5 \dot{i} + \dot{j}|=\sqrt {0.5^2+1^2}\approx 1.1 $
The area of the opening of the rain gauge is $1.1$ square inches.
(b) $ V =| \textbf R \cdot \textbf A$|= |$(\dot{i} -2 {j}) \cdot (0.5 \dot{i} + \dot{j})| = | 1\times 0.5-2\times1 |=|-1.5|=1.5$.
The volume of rain was $1.5 \text{ in}^3$.
