Magnitude of cross product

I am trying to find the magnitude of the cross product C. I tried using norm but that didn't give me the write answer. Also, how would you simplify the k component, with trig dentities?

syms theta phi
r = [2.*sin(phi).*cos(theta) 2.*sin(phi).*sin(theta) 2.*cos(phi)]

r = 

P=diff(r,theta)

P = 

R=diff(r,phi)

R = 

C = cross(R,P)

C = 

Answer 1

[John D'Errico]

syms theta phi
r = [2.*sin(phi).*cos(theta) 2.*sin(phi).*sin(theta) 2.*cos(phi)];
P=diff(r,theta);
R=diff(r,phi);
C = cross(R,P)

C = 

Why not try simplify? It might work.

C = simplify(C)

C = 

So a simplify helped. Never assume that ALL computations end with a simplfy.

Norm can introduce some problems, because norm feels the need to introduce an absolute value in there.

norm(C)

ans = 

But what is the 2-norm of a vector, but a sum of squares of elements, and then a sqrt?

normsquared = simplify(sum(C.^2))

normsquared = 

And that is getting pretty close.

sqrt(normsquared)

ans = 

And there is still a minor problem here, probably because MATLAB is not certain that sin(phi)^2 is a positive number. We can tell it that, by telling MATLAB that phi is itself real valued.

assume(phi,'real')
simplify(sqrt(normsquared))

ans = 

That seems reasonable now. Symbolic tools just need a little gentle persuasion at times.