Warm up: Find a vector that is perpendicular to (1, 2, 5) and (4, 1, 2)

Cross Product of Two Vectors

Section 7.6

The Cross Product of Two Vectors• The cross product of two

vectors produces a vector that is perpendicular to both vectors, and is written a x b

Try: Show that (a1,a2,a3)x(b1,b2,b3) is equal to:

Calculating the Cross Product

• For vector a = (1, 2, 1) and b = (4, 1, 2), calculate:

a) a x b

Reminder:

• What is the cross product?

• What does it produce?

• How do you calculate it?

• Where does this formula come from?

Calculating the Cross Product• For vector a = (1, 2, 1)

and b = (4, 1, 2), calculate:

a) a x b

b) b x a

c) What is different about these?

Applications of the Cross Product

a) Find the area of the parallelogram defined by the vectors (5, 1, -2) and (3, -2, 2):

Applications of the Cross Product

a) Find the area of the parallelogram defined by the vectors (5, 1, -2) and (3, -2, 2):

b) Find the magnitude of (5, 1, -2) X (3, -2, 2)

Problem: Find two vectors whose cross product is the 0 vector.

• What does it mean to have a cross product equal to the zero vector?

Reasoning with Properties of the Cross Product

• True or false: (a x b) x c = a x (b x c) for all vectors a, b and c in R3.

Summary:• What does the cross product represent?

• What is an easy way to remember the formula for the cross product?

• How are a x b and b x a different?

• What does it mean to have a cross product equal to the 0 vector?

• Practice: Pg. 407, #1, 3, 4, 9, 11, 13