1. The problem statement, all variables and given/known data x,y, z are vectors in R^n. We have the equation: ax +by +cz, where a,b,c are constants such that a+b+c=1, and a,b,c>=0 What is the geometric interpretation of the equation? 2. Relevant equations sv + tu, where u,v are vectors in R^n and s,t are constants such that s+t=1, s,t>=0 geometrically represents a line between u,v. 3. The attempt at a solution So by similar logic, would ax +by +cz be a line through x,y,z?