In some sense, this activity considers the reverse problem of that considered in Activity 13.12.4. Here, each part of the activity gives you an oriented simple closed curve \(C\) in \(\R^3\text{,}\) and your task is to find
a surface \(S\) so that \(C\) is the boundary of \(S\) and
a normal vector for the \(S\) so that a person walking along \(C\) in the direction of the given orientation with head pointing in the direction of your chosen normal vector would have their left hand over \(S\text{.}\)
You are encouraged to think about multiple possible answers, since as we saw in Preview Activity 13.12.1, there may be more than one reasonable choice of a surface with a particular boundary.
The curve \(C\) is the triangle with vertices \((1,0,0)\text{,}\)\((0,1,0)\text{,}\) and \((0,0,1)\) with orientation corresponding to the order the points are listed here.