Tangent for 3D vectors

Dear All,

I am developing a 3D car game in C++ using openGL. To calculate the
Ground Velocity, I need the formula to calculate tangent for 3D
vector. I got the tangent for  2D vector from some game samples (i.e.,
Tangent for 2D vector (x,y) = (-y,x)). Please help me to find out the
tangent for 3D vector.

Thanks in advance.

Regards,
Kalai