Chapter 13 - Partial Derivatives - 13.1 Functions Of Two Or More Variables - Exercises Set 13.1 - Page 916: 62

Result : See proof

For the function \(f(x,y,z) = 3x - y + 2z\), the level surfaces are represented by: \[ f(x,y,z) = k, \quad k \in \mathbb{Z} \] \[ 3x - y + 2z = k \] This is the equation of a plane, so the level surfaces are parallel planes with the same normal $3\text{i}-\text{j}+2\text{k}$.