Finding the Curvature of a Plane Curve

[goomer]

Find the curvature of the plane curve given by r(t) = (3cost)i + (3sint)j at the point (√(2), √(7) ).

I know that κ=|r'(t) x r"(t)| / |r'(t)|^3
However, I believe that you are not allowed to do cross product unless there is an x, y, and z component and this question only has an x and y component.

In this case, am I supposed to use κ= |T'(t)/r'(t)| instead or use another formula all together?

 

[LCKurtz]

Just add a 0k to your vector and treat it as 3D if you want to use the cross product.