Use the vector field, \( \vec{F} = \frac{\vec{r}}{|\vec{r}||^3} \), to answer the questions below. In each case, show work and simplify your final answer.
(A) Express \( ||\vec{F}|| \) in terms of x, y, z. For example, you might write \( ||\vec{F}|| = x + y + z \) for your answer.
(B) Express \( \vec{F} \cdot \vec{r} \) in terms of x, y, z.
(C) Find a unit vector parallel to \( \vec{F} \) and pointing in the opposite direction in terms of x, y, z.
(D) Express \( \vec{F} \) as a vector-valued function of t if \( \vec{r} = cos(t)\vec{i} + sin(t)\vec{j} + \vec{k} \). For example, you might write \( \vec{F} = t\vec{i} + t^2\vec{j} + sin(t)\vec{k} \) for your answer.
