Makes sense. Now I have |B|. To get the components of \vec{B}, I can use
0 = A_{x} B_{x} + A_{y}B_{y}+ A_{z}B_{z}
and
0 = C_{x} B_{x} + C_{y}B_{y}+ C_{z}B_{z},
and
B^{2} = B_{x}^{2} + B_{y}^{2} + B_{z}^{2} .
Does that sound right?
I have a vector equation:
\vec{A} \times \vec{B} = \vec{C} . \vec{A} and \vec{C} are known, and \vec{B} must be determined. However, upon trying to use Cramer's rule to solve the system of three equations, I find that the determinant we need is zero. I know now that I need to choose a...
Here's my definition of temporal average -
<f(t,x)> = \stackrel{lim}{T\rightarrow\infty} \frac{1}{T} \int_{t_{0}}^{t_{0}+T} f(t,x) dt
And it's all making even less sense to me now. With this definition, <f(t,x)> is...
That's it actually. But all the math texts I saw move differentiation past the integral sign only when the two involve independent variables. Is there a rigorous justification for doing it when both the differentiation and integration involve the same variable?
Edit - I just cant get the latex...
I've been studying Turbulence, and there's a lot of averaging of differential equations involved. The books I've seen remark offhandedly that differentiation and averaging commute
for eg. < \frac{df}{dt} > = \frac{d<f>}{dt}
Here < > is temporal averaging. If...