A parallelepiped is a three-dimensional shape that has six faces, each of which are parallelograms. It is similar to a cube or rectangular prism, but its faces are not necessarily square or rectangular.
A parallelepiped is formed by using three non-collinear vectors, which means that the vectors are not in the same line. These vectors serve as the edges of the parallelepiped, and their length and direction determine the shape of the parallelepiped.
The vectors used to form this parallelepiped are u = (-2,3,5), v = (4,2,8), and w. These three vectors are not collinear, and their lengths and directions determine the shape and size of the parallelepiped.
No, the vectors used to form a parallelepiped must follow certain rules in order for the shape to be considered a parallelepiped. The vectors must be non-collinear, and their lengths and directions must be able to form a closed shape with six faces that are all parallelograms.
Using vectors to form a parallelepiped allows for the shape to have specific properties, such as having six faces that are all parallelograms. This also allows for the shape to be used in various mathematical and scientific calculations, as the properties of vectors can be applied to the parallelepiped.