1. The Cross Product

2. We have two ways to multiply two vectors. One way is the scalar or dot product. The other way is called the vector product or cross product. Cross Product If then

3. Finding the cross product using the determinant form: If then

4. Given the following vectors below, find Answer:

5. Given the following vectors below, find Answer:

6. Algebraic Properties of the Cross Product:

7. If what is? What does this mean? This means that the cross product is a vector which is orthogonal to the two vectors.

8. This also means that: if and only if the two vectors are scalar multiples of each other. This means that the two vectors are parallel to each other.

11. If then: and If then:

12. Find the volume of the parallelepiped with the vectors given below: Answer: Volume = 36

13. Find the area of the triangle with the given vertices: A(2, -1, 1), B(-1, 3, 2), C(-2, 3, 1) Answer:

14. Find the area of the triangle with the given vertices: A(2, -7, 3), B(-1, 5, 8), C(4, 6, -1) Answer:

15. Find the area of the parallelogram with the given vertices: A(1, 1, 1), B(2, 3, 4), C(6, 5, 2), D(7, 7, 5) Answer:

16. Given the following vectors below, find: Answer: 41 M03/HL1/3 Given the following vectors below, find: Answer: 23 M04/HL1/8/TZ1

17. Let Find the value of p, given that is parallel to c. Answer: p = 4 M06/HL1/11

18. Consider the points A(1, 2, -4), B(1, 5, 0) and C(6, 5, -12). Find the area of the triangle ABC. Answer: 21.9 N03/HL1/1