Final answer:
This high school-level mathematics question requires finding points on a 3D line that are at a unit distance from a 2D line, using geometry and algebra.
Step-by-step explanation:
The question asks to find all points on the line represented by the equation 3x + y² - z = 0 that lie at a unit distance from the line 3x + 4y = 7. This is a geometry problem that involves three-dimensional space and distance calculations between a line and a point.
To solve this, one needs to apply concepts of geometry and algebra to find the points that satisfy both the equation of the given line and the condition of being at a unit distance from the second line. The solution involves setting up an equation for the distance from a point to a line in two dimensions and incorporating the constraint given by the three-dimensional line equation.