Polar coordinates explanation needed on calculation [closed]

This is the question.

Here is the answer. But honestly I cant figure it out. Maybe my lecturer's handwriting is quite illegible too (just kidding). Sorry if I ask too simple question but seriously I want a clarification on this. Thanks :)

• What do you mean by the unit vector, which unit vector? What are you trying to say with direction of increment? – Mussé Redi May 31 '14 at 15:01
• @MusséRedi edited ard. sorry :) – user47593 May 31 '14 at 15:06

For $(a)$, start working out the right sides. For $(b)$, use the chain rule and notice that $\frac{\mathrm d}{\mathrm{dt}}\hat{\mathbf i} = 0$ and $\frac{\mathrm d}{\mathrm{dt}} \hat{\mathbf j} = 0$.
The easiest way is to start with the equation $$\frac{d \vec{A}}{dt} = \vec{\omega} \times \vec{A},$$ which holds when $\vec{A}$ is rotated with instantaneous angular velocity $\vec{\omega}$ and leads to the equations above if you embed the plane in euclidean space of dimension 3.