Find equations for the tangent line to the curve
at the point (1,-1,3)
Okay, if I can find parametric equations representing this curve I can easily find a tangent vector along the curve at the point (1,-1,3) by simply differentiating my parametric equations.
At this point I'll have a tangent vector along the curve, I want a tangent line to the curve at the point (1,-1,3), so I'll simply define a new line that points in the direction of my tangent vector, starting at the point (1,-1,3).
Problem is, I can't seem to find a reasonable way of finding parametric equations for the curve.
Any ideas?
EDIT: I've solved it by taking the gradient of both functions F(x,y,z) = 0 and G(x,y,z) = 0 evaluated at the point (1,-1,3) and taking the cross product between to produce my vector along the tangent line.