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

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

What is the cross product?

What?

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?

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

Geometric Properties

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

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?

The Triple Scalar Product

Geometric Properties

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

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