Here are the visual representations of the problems:

1. Triangle (Problem 5): The vectors $\vec{a}$ (red) and $\vec{b}$ (blue) form the two sides of the triangle. The area of the triangle is $0.87$ square units.

2. Parallelepiped (Problem 6): The three vectors $\vec{A}$ (red), $\vec{B}$ (green), and $\vec{C}$ (blue) define the edges of the parallelepiped. The volume of this shape is $20$ cubic units.

Let me know if you need further details or clarification!

Follow-up questions:

1. How is the cross product used to find the area of a parallelogram or triangle?
2. Can the scalar triple product be used to find the volume of any shape?
3. How do vector magnitudes influence the shape of the parallelepiped?
4. What is the physical interpretation of the dot and cross products in real-world problems?
5. How would you extend this method to higher-dimensional vector spaces?

Tip: The cross product is only defined in three dimensions, but the concept of area and volume extends to higher dimensions with more general forms of the cross product.