The image contains two types of problems related to vectors in three-dimensional space:

Problem 32 (Parallelogram Area)

Find the area of the parallelogram given by the vertices $(1, -2, 3)$, $(2, 0, 1)$, and $(0, 4, 0)$. To calculate this:

1. Determine two vectors representing the sides of the parallelogram.
2. Compute the cross product of these two vectors.
3. Take the magnitude of the resulting vector (this gives the parallelogram's area).

Problem 47 (Parallelepiped Volume)

Calculate the volume of the parallelepiped determined by vectors $\overrightarrow{PQ}$, $\overrightarrow{PR}$, and $\overrightarrow{PS}$, where the points are:

• $P = (2, 1, -1)$,
• $Q = (-3, 1, 4)$,
• $R = (-1, 0, 2)$,
• $S = (-3, -1, 5)$.

To solve:

1. Compute the vectors $\overrightarrow{PQ}$, $\overrightarrow{PR}$, and $\overrightarrow{PS}$.
2. Find the scalar triple product of these vectors.
3. Take the absolute value of the scalar triple product (this gives the volume).

Would you like me to solve both problems step-by-step?