Thread: Tangent Vector to a Space Circle

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.

The normal vector to the tangent plane to the sphere is .

The normal vector of the given plane is p=(1,1,1).

The vector perpendicular to and is (cross product)