The surface z=f(x,y)=√(9-2x2-y2) and the plane y=1 intersect in a curve. Find parametric equations for the tangent line at (√(2),1,2).
The Attempt at a Solution
Okay, so I'm just trying to work through an example in my textbook, so technically I have the answer, I just want the in between steps that I can't figure out. I know that you take the partial derivative with respect to x and get
and then you plug in the given point (√(2),1,2) and come out with -√(2). But then it goes to say, 'It follows that this line has direction vector <1,0,-√(2)>'.
Where did the 1 and 0 come from? And how do I get the parametric equations from the 'direction vector'?