# Question:CrossProduct

## Question:CrossProduct

Maple
I'm trying to use Maple to calculate surface integral; before getting to the surface integral, I need to get cross product of two vectors; but I could not get the codes work. Please help.

with (VectorCalculus):

x:= (r,t) -> r*sin(t);
y:= (r,t) -> r*cos(t);
z:= (r,t) -> r^2.sin(t)*cos(t);

> R := Vector*[x(r, t), y(r, t), z(r, t)];

Vector [r sin(t), r cos(t), r sin(t) cos(t)]
> r1 := VectorField(diff(R, r));
VectorField([0, 0, 0] + Vector [sin(t), cos(t), 2 r sin(t) cos(t)])
>
> r2 := VectorField(diff(R, t));
VectorField([0, 0, 0] + Vector [r cos(t), -r sin(t), r^2 cos(t) - r^2 sin(t) ])
>
>
> dS := CrossProduct(r1, r2);
/
CrossProduct\

VectorField([0, 0, 0] + Vector [sin(t), cos(t), 2 r sin(t) cos(t)]),

/
VectorField\[0, 0, 0]

+ Vector [r cos(t), -r sin(t), r cos(t) - r sin(t) ]//
>

How do I get maple to output what the cross product looks like?

(I know how to take the cross product by hands, wanted to see the result from Maple).

Thanks.

--mdc

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