1 / 7

The Vector Cross Product

The Vector Cross Product. Definition. The cross product of two 3-d vectors becomes a 3-d vector itself. The cross product is:. Example. Method 1. An easier method is to use the formula listed in the matrices part of the formula sheet. Method 2.

Download Presentation

The Vector Cross Product

An Image/Link below is provided (as is) to download presentation 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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The Vector Cross Product

  2. Definition The cross product of two 3-d vectors becomes a 3-d vector itself. The cross product is: Example Method 1 An easier method is to use the formula listed in the matrices part of the formula sheet. Method 2

  3. Applications of vxw - the perpendicular vector The resulting vector of the cross product of vxw will always be perpendicular to v and w, as shown in the diagram below. Find the vector that is perpendicular to: 1. and 2. 3i + 2j - k and 3j - 5k. -7i + 15j + 9k

  4. Applications of vxw - the area of a triangle or parallelogram Area of a triangle is given by . If a and b are vectors the area of a triangle becomes: Proof: Expand and simplify

  5. So that proof means: The area of a triangle where a and b are vectors is given by:

  6. Find the area of the triangle with vertices A(1,1,2) B(-1,3,2) and C(4,1,5). Find two sides of the triangle, the vectors AB and AC. The area is given as follows: and Now find the cross product of the two vectors:

  7. TRY THESE YOURSELF Find the area of the triangle with vertices A(2,7,3), B(-8,3,1) and C(1,6,-2). Find two perpendicular unit vectors to the plane containing the points (4,1,3), (1,1,2) and (7,2,-4).

More Related