\int [a(\dot{b}\cdot a + b\cdot\dot{a}) + \dot{a}(b\cdot a) - 2(\dot{a}\cdot a)b - \dot{b}|a|^2]\, dt
The above are all vectors. How would one go about integrating this, the answer is apparently
a \times (a \times b) + h
where h is a constant vector
I don't quite see how they arrive at...
I'm stuck on a problem on vector calculus.
Given a surface S defined as the end point of the vector:
\mathbf{r}(u,v) = u\mathbf{i} + v\mathbf{j} + f(u,v)\mathbf{k}
and any curve on the surface represented by
\mathbf{r}(\lambda) = \mathbf{r}(u(\lambda),v(\lambda))
and it mentions the...
I got as far as needing to show that if both a and b are not divisble by three then a^2 + b^2 must not be divisible by 3, but that's exactly where i got stuck,all attempts to show this have proved dead ends :(
*edit*
what i have managed to show is that if:
a not divisible by 3 => a%3 = 1 or 2...
I'm stuck on a seemingly simple part of a proof (a proof showing there are no non zero solutions of the equation a^2 + b^2 = 3(s^2 + t^2)
at one step it says if
a^2 + b^2 = 3(s^2 + t^2) this implies
both a and b must be divisible by 3.
I tried to prove this myself but have had no...