# How to define vector function in Mathematica

• Mathematica
How you define vector function in Mathematica?

For example, f is a vector function and f=(xy,yz,zx). How to define this in Mathematica and then how to calculate the value of the components of f for any number x, y, and z?

For scalar functions it goes as this:

f[x_]:=x^2
f[4]

Any idea for vectors?

Can you use this to get you started?

You could define this to be just what your definition said:

f[v_List]:={v[[1]]*v[[2]],v[[2]]*v[[3]],v[[3]]*v[[1]]}

The {} around your result says your f is returning a vector and you calculate each element of that vector.

Or you can use tricky coding that just happens to do the same thing in this particular case.

In[1]:= f[v_List]:=RotateLeft[v]*v;

In[2]:= f[{x,y,z}]
Out[2]= {x y,y z,x z}

In[3]:= f[{3,Pi,-2}]
Out[3]= {3 Pi,-2 Pi,-6}

Last edited:
You could define this to be just what your definition said:

f[v_List]:={v[[1]]*v[[2]],v[[2]]*v[[3]],v[[3]]*v[[1]]}

Or you could define this as

f[{x_,y_,z_}]:={x y,y z,z x}

if that would be easier to understand

There are at least a dozen different ways of doing almost anything in Mathematica

Thank you very much :)