Recent content by Ceres629

  1. C

    Graduate Proving the Linear Independence of Coordinate Curves on a Smooth Surface

    thanks tiny tim, your answer also makes sense.
  2. C

    Graduate How to Integrate Complex Vectors Using the Vector Triple-Cross-Product Formula?

    \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...
    • Ceres629
    • Thread
    • Expression Integral Vector
    • Replies: 1
    • Forum: Calculus
  3. C

    Graduate Proving the Linear Independence of Coordinate Curves on a Smooth Surface

    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...
  4. C

    Graduate Prove a^2 + b^2 = 3(s^2 + t^2) implies both a and b must are divisible by 3

    Ah okay, thanks for the pointer GreatHouse and thanks for the confirmation Gokul. :smile:
  5. C

    Graduate Prove a^2 + b^2 = 3(s^2 + t^2) implies both a and b must are divisible by 3

    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...
  6. C

    Graduate Prove a^2 + b^2 = 3(s^2 + t^2) implies both a and b must are divisible by 3

    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...