Can someone help me with the following question. I've been having trouble with problems of this kind for a while now.(adsbygoogle = window.adsbygoogle || []).push({});

Q. If the path u(t) (u is a vector) is differentiable at least three times, simplify:

[tex]

\frac{d}{{dt}}\left[ {\left( {u' \times u''} \right) \bullet \left( {u' - u} \right)} \right]

[/tex]

I can't remember the properties of the dot product but I know that the dot product is an inner product. So I will start by using the distributivity of the inner product.

[tex]\frac{d}{{dt}}\left[ {\left( {u' \times u''} \right) \bullet \left( {u' - u} \right)} \right][/tex]

[tex]

= \frac{d}{{dt}}\left[ {\left( {u' \times u''} \right) \bullet u' - \left( {u' \times u''} \right) \bullet u} \right]

[/tex]

It's not much but it's all I've got at the moment. The cross product will produce a single vector so there probably isn't much that I can do with it. Each of the two expressions inside the square bracket are scalars (scalar functions of t is probably the more accurate description) so I can probably continue as follows.

[tex]

= \frac{d}{{dt}}\left[ {\left( {u' \times u''} \right) \bullet u'} \right] - \frac{d}{{dt}}\left[ {\left( {u' \times u''} \right) \bullet u} \right]

[/tex]

Ok well I'm really stuck here. Does anyone have any suggestions? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Homework Help: Differentiation and dot product

**Physics Forums | Science Articles, Homework Help, Discussion**