# Solutions to Problem Set 4

Math 311-01/02

1-30-2018

[Cross product]

1. Compute the cross product of and .

2. Compute the cross product of and .

3. Compute the cross product of and .

4. Compute the cross product of and .

5. Find two unit vectors perpendicular to both of the vectors and .

The two unit vectors are .

6. The vectors and form adjacent sides of a parallelogram. Find the area of the parallelogram.

The area is

7. The vertices of a parallelogram, listed counterclockwise, are , , , and . Find the area of the parallelogram.

The vectors for the sides adjacent to A are

The area is

8. Find the volume of the parallelepiped with edges determined by the vectors , , and .

The volume is 3.

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