Final Answer:
The volume of the parallelepiped for the given values of p, q, and s is V = |p · (q × s)|, where |p · (q × s)| represents the magnitude of the scalar triple product of vectors p, q, and s.
Step-by-step explanation:
To determine the volume of a parallelepiped with the given values of vectors p, q, and s, we can use the formula for the volume in terms of the scalar triple product. The volume V is given by the magnitude of the scalar triple product of the three vectors, which can be expressed as V = |p · (q × s)|. Here, p · (q × s) represents the scalar triple product of vectors p, q, and s. The magnitude |p · (q × s)| gives us the volume of the parallelepiped formed by these vectors.
In this context, the scalar triple product p · (q × s) is calculated as the dot product of vector p with the cross product of vectors q and s. The result is a scalar quantity that represents the signed volume of the parallelepiped formed by these three vectors. Taking its magnitude gives us the absolute value of this signed volume, which represents the actual volume of the parallelepiped without considering its direction.
By using this approach, we can accurately determine the volume of a parallelepiped based on the given values of vectors p, q, and s without needing to calculate individual components or dimensions separately.