Page Description Equation
922 equation of the line tangent to the curve formed by the intersection of two surfaces $f\left(x,y,z\right)=0$ and $g\left(x,y,z\right)=0$ at the point $\vect{r}\left(t\right)=P_0\left(x_0,y_0,z_0\right).$ \[ \vect{r}\left(t\right)=\vect{r}_0+t\vect{v}\\ \text{where}\\ \vect{v}=\nabla f\times\nabla g\\ x=x_0+tv_1\\ y=y_0+tv_2\\ z=z_0+tv_3 \]

Notes

Page Notes
Gradient Vector (Definition):
Gradient Vector (Computational Formula):
Directional Derivative
Direction of zero change. If $\nabla f\cdot\vect{u}=0$ then $u$ is the direction of zero change.
Lines tangent to level curves. orthogonal vector. gradient vector.
Estimating Change in $f$ in direction $\vect{u}.$