Method to parameterize circles in R3 laying in a plane

dispiriton

Homework Statement

In general how do i parametrize a circle of radius r at centre (a,b,c) laying on a plane? E.g. (x + y + z = 6)

The Attempt at a Solution

$$R(t) = \langle a,b,c\rangle +r \vec u \cos(t) + r\vec v \sin(t)$$