question_answer

The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If \[\frac{{{\varepsilon }^{2}}\sqrt{{{R}^{2}}+{{\left( L\omega -\frac{1}{C\omega } \right)}^{2}}}}{R}\] is the time for the planet to move from C to D and \[\frac{{{\varepsilon }^{2}}\left[ {{R}^{2}}+{{\left( L\omega -\frac{1}{C\omega } \right)}^{2}} \right]}{R}\] is the time to move from A to B, then

A) \[\frac{{{\varepsilon }^{2}}R}{\sqrt{{{R}^{2}}+{{\left( L\omega -\frac{1}{C\omega } \right)}^{2}}}}\]

B)                        \[V=-{{x}^{2}}y-x{{z}^{3}}+4\]   

C)        \[\overrightarrow{E}\] 

D)        \[\overrightarrow{E}=\hat{i}(2xy+{{z}^{3}})+\hat{j}{{x}^{2}}+\hat{k}3x{{z}^{2}}\]