1. I was reading on the geometric interpretation of the grad operator. I've did until the point where this particular relation was given.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]d\varphi=0=C_1-C_1=\Delta C=(\nabla \varphi)\bullet d \vec r [/tex]

This is when we permit [tex] \vec r [/tex] to take us from the surface [tex] \varphi (x,y,z)=C_1[/tex] to another adjacent surface [tex]\varphi (x,y,z)=C_2 [/tex] where c are constants.

Why is it that in the first equation we have [tex] C_1-C_1[/tex] ?? Also, why is it that the consequence of the first relation shows that,

for a given [tex]\vert {d\vec r}\vert[/tex], the change of [tex] \varphi [/tex], [tex] d \varphi [/tex] is maximum when [tex]\vert {d\vec r}\vert[/tex] is parellel to [tex] \nabla\varphi [/tex] when [tex] \nabla\varphi [/tex] is normal to the surface.

2. While evaluating the divergence of vector, [tex] \nabla \bullet \vec r f(r) = \frac {\partial}{\partial x} (xf(r))+ \frac {\partial}{\partial y}(yf(r))+ \frac{\partial}{\partial z} (zf(r)) [/tex],

why is it equivalent to,

[tex] 3 f(r)+\frac {x^2}{r} \frac {df}{dr}+\frac {y^2}{r} \frac {df}{dr}+\frac {z^2}{r} \frac {df}{dr} [/tex] ????

I've tried manipulating the partial differentials using chain rules and all but don't seem to get it. Can someone show me the steps how? Also,

3. I was trying to simplify[tex]\nabla \times f \vec v \vert _x = \frac {\partial}{\partial y} (f V_z)-\frac {\partial}{\partial z} (f V_y)[/tex]. Also, how does it reduce to the final answer,

[tex] f \nabla \times \vec V \vert _x +\nabla f \times \vec V \vert _x [/tex]??

I have also tried manipulating the partial derivatives to no avail. Can someone help??? thanks alot....

: )

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A few Vector calc questions.

Loading...

Similar Threads for Vector calc questions | Date |
---|---|

Vector calc identities | Oct 11, 2013 |

Math methods in physics book - vector calc proof | Jan 14, 2013 |

Vector Calc: Can you verify my answer? | Jun 7, 2009 |

Vector calc proof question | Sep 22, 2008 |

Vector Calc Questions | Sep 21, 2008 |

**Physics Forums - The Fusion of Science and Community**