Science:Math Exam Resources/Courses/MATH152/April 2017/Question A 11/Solution 1

The location of $sa+(1-s)b=b+s(a-b)$ can be thought of as the endpoint of the vector sum of ${\vec {b}}$ and $s({\vec {a}}-{\vec {b}})$ as shown below. Notice that $s({\vec {a}}-{\vec {b}})$ is a scaled version of ${\vec {a}}-{\vec {b}}$, and since $0\leq s\leq 1$, its length ranges between 0 and the full length of ${\vec {a}}-{\vec {b}}$.

Hence the set in question is simply a line segment between ${\vec {b}}$ and ${\vec {a}}$: