Answer
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Work Step by Step
Step 1: In this problem, we have to give examples of vector quantities that not only depend on position but also on time. Step 2: Mentioned below are three vector quantities that are functions of time, in addition to the position in space: (1) The velocity and acceleration functions in a flow of liquid. Each point will have a different set of velocity and acceleration vectors at different points in time. Just like liquids, electromagnetic waves, and sound also propagate through space and time: (2) The electric and magnetic field intensity in space. (3) The sound waves through a 3-dimensional medium. To address this, we define \(\vec{r}(t) = \langle x(t), y(t), z(t) \rangle\) as functions of time or provide a relationship between time and position that effectively does the same.
