Find a vector equation for the tangent line to the curve of intersection of the cylinders
$\ x^2 + y^2 = 25$ and $\ y^2 + z^2 = 25$
at the point (3,4,2).
I don't understand the answer key. I've explained my interpretations below. Could someone clarify:
Why is the projection of C onto the xy plane:$\ x^2 + y^2 = 25$. I understand that a projection in 3D space is the "shadow" of the graph onto one plane, but I don't quite see that C's projection can be modeled as given.
Why is z >= 0?