Calculus and vectors
posted by Jake .
Could someone explain to me how I can find the area/perimeter/volume of a rectangular prism if I am given R^3 points. For example find area of rectangular prism given pts (2,3,4)(5,3,2), similar to this.
As it is, there are multiple solutions if the sides of the prism can orient in any direction. Since the two points define only a diagonal, which can fit many prisms.
This problem can be solved if there were the requirement that the sides of the prism are parallel to the coordinate axes.
Assuming that this is the case, then the sides of the prism parallel to the x, y and z-axes are respectively:
|x2-x1|, |y2-y1| and |z2-z1|
which are 3, 0, -2 respectively.
So the prism is flat like a piece of paper, and area, volume=0.