Is there a way to find the normal plane and the tangent line to the following surfaces without having a point of intersection, I know you can use Newton-Raphson method to find the approximate intersection point but, is there any way or is even possible?
$$ 1) \hspace{0.3cm} x^2 + y^2 + z^2 = 14 $$ $$ 2) \hspace{0.3cm} x + y + z = 6$$