2. (16 points) Assume a typical Cartesian coordinate system and let \(\vec{r} = (25\text{ m}, 41^\circ \text{ above the positive }x\text{-axis})\).
(a) Draw a diagram of the vector \(\vec{r}\).
(b) What is the z component of \(\vec{r}\)? Note that vector components are scalars!
(c) What is the y component of \(\vec{r}\)?
(d) Write \(\vec{r}\) using the unit vectors \(\hat{i}\) and \(\hat{j}\).
(e) Write \(\vec{r}\) using the unit vectors \(i\) and \(j\).
(f) Write \(\vec{r}\) using angle-bracket notation (, ).
(g) Let \(\vec{s} = 4.2\hat{x} - 24.3\hat{y}\). What is the magnitude of \(\vec{s}\) (denoted \(|\vec{s}|\) or \(s\))?
(h) Find \(3.1\hat{s} - 4.6\vec{r}\).
