Final answer:
The level surfaces of f(x,y,z)=sin(x+y+z) can be described as a family of parallel planes that are perpendicular to the direction (1,1,1) in three-dimensional space.
Step-by-step explanation:
The level surfaces of the function f(x,y,z)=sin(x+y+z) can be described as a family of parallel planes that are perpendicular to the direction (1,1,1) in three-dimensional space.
These planes are separated by a fixed distance of one unit along this direction. As the values of x, y, and z change, the sine function will change, resulting in different level surfaces.
For example, when the function evaluates to sin(0), the level surface will be a plane passing through the origin.