Find a vector tangent to the space circle:
At the point
I should know how to do this, but it's been 4 years since I had multivariable calc and I don't remember a darn thing from that class. :-(
Since the circle belongs to the plane x + y + z = 0, the tangent vector belongs to it as well. Also, the vector is perpendicular to the radius-vector . So you have two equations: x + y + z = 0 and x + 2y - 3z = 0. I get (-5, 4, 1) up to proportionality.