1. 11.3 The Cross Product
Objective: Find the cross product of
two vectors in space and use the
geometric properties of the cross
product.
Standard: Linear Algebra 10.0

2. Quick Review:
Find u·v if u=-4i+3k and v=5i+6j-2k

3. What is the cross product?
What?

4. Ex. 1) Given u=2i+j+3k and v=i+3j+2k, find:
a) u x v
b) v x u
What do you notice?

5. Ex. 2) Find ||u x v|| if u=-3i+4j-2k and
v=2i-2j+6k.

6. Geometric Properties

7. Ex. 3) Find a unit vector that is
orthogonal to both u=3i-4j+k and v=-3i+6j.

8. Ex. 4) Show that the quadrilateral with vertices A(3, 5, 0),
B(1, 2, 4), C(1, 3, 4) and D(3, 6, 0) is a parallelogram then
find it's area. Is the parallelogram a rectangle?

9. The Triple Scalar Product

10. Geometric Properties

11. Ex. 5) Find the volume of the parallelepiped
having u=3i-5j+k, v=2j-2k, and w=3i+j+k.

12. Assignment:
#17 p. 832 #5, 9, 22, 23,
29, 34, 35, 38, 39, 42
- Quiz 11.3 on Thurs/Fri
- π Day on Monday
- Ch. 8 & 11 Test on
Thurs/Fri Mar. 17-18