the line through the points p and q is formed with "p + λ(q − p)." Why is the direction given by q-p and not q+p or something else

The expression "p + λ(q - p)" represents a parametric equation for a line passing through points P and Q, where p and q are positive vectors of P and Q and λ is a parameter that varies to trace points along the line.

The direction vector q - p is used because it describes the direction from point P to point Q. By substrating P from Q, you get a vector pointing from P to Q. By multiplying this direction vector by λ and adding it to point P, you can traverse the line in the direction from P to Q.