Recent content by LFCFAN

A = {2,1,2,4} B = {4,1,6,2} angle = arccos( (A.B)/(norm(A)*norm(B)) ) area = (1/2)A.B sin(angle) Is this correct? if yes, it is easy to generalize for Rn.

I've literally typed out the question as it has been given. I think take it as a standard triangle in n-dim space

Some elaboration on that would help, is possible?

? Let me know if I've explained the problem sufficiently

Find the area of the triangle with sides A = (a1 ... an) B = (b1 ... bn) and A-B = (a1-b1 ... an-bn) I don't even know where to start. I know how to do it in 3D with the cross product, but that obviously won't work for higher dimensions. So I need help generalizing for Rn.

bump

Homework Statement How to find area of an n-dimensional triangle using vectors? Homework Equations The Attempt at a Solution

Any mathematical elaboration I can have?

Homework Statement Why does the following ODE ALWAYS have two linearly independent solutions? x''(t) + a(t) x'(t) + b(t) x(t) = f(t) The characteristic polynomial argument is not sufficient?

Thanks a lot man. But what I've done is correct, right? Literally can go on to find equations of motion with my lagrangian?

Thanks. Would it be similar for all y=f(x)?

Hello fellow PF members I was wondering how one would go about finding the lagrangian of a problem like the following: A particle is constrained to move along the a path defined by y = sin(x). Would you simply do this: x = x y = sin(x) x'^2 = x'^2 y'^2 = x'^2 (cos(x))^2...

Yes that's the equation, just swop t for x.How have I done it wrong? I cross-checked with peers...

partial derivative of (y')^2/y wrt y = - (y')^2/y^2 partial derivative of (y')^2/y wrt y' = (2 y' y'')/y derivative of (2 y' y'')/y wrt x = (2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'')/y^2 finsihed. everything I've done is correct

I've done it wrong because you can't solve the equation... right...