MAT 1236 Calculus III

1 / 30

# MAT 1236 Calculus III - PowerPoint PPT Presentation

MAT 1236 Calculus III. Section 12.4 The Cross Product. http://myhome.spu.edu/lauw. HW…. WebAssign 12.4 Read 12.5 ( Seriously! ): The first not too easy section in Calculus. Preview. Define a new operation on vectors: The Cross Product

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' MAT 1236 Calculus III' - cedric

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### MAT 1236Calculus III

Section 12.4

The Cross Product

http://myhome.spu.edu/lauw

HW…
• WebAssign 12.4
• Read 12.5 (Seriously!): The first not too easy section in Calculus
Preview
• Define a new operation on vectors: The Cross Product
• Unlike the dot product, the cross product of two vectors is a vector.
• Properties of the cross product.
We are Interested in …
• Given 2 vectors, they “span” a plane
• Find a vector perpendicular to this plane
The Cross Product

If and , the cross product of a and b is the vector

The Cross Product

The formula is traditionally memorized by using (formal) determinant expansions

The Cross Product

The formula is traditionally memorized by using (formal) determinant expansions

Expectations
• You are expected to use the above standard procedure to find the cross product.
• You are expected to show all the steps. Keep in mind, good practices are key to minimize the chance of making mistakes.
Property B

In addition, the cross product obeys the Right Hand Rule.

In Particular

is in the same direction of k and

Property D

Two nonzero vectors and are parallel if and only if

Property D (Why?)

Two nonzero vectors and are parallel if and only if

Property E

The length of the cross product axb is equal to the area of the parallelogram

determined by a and b.

Example 2

Find a vector perpendicular to the plane that passes through the points

P(6,0,0) , Q(1,1,1), R(0,0,2)

Example 3

Find the area of the triangle with vertices

P(6,0,0) , Q(1,1,1), R(0,0,2)

Other Properties

Right Hand Rule

Default

Reference only