http://www.ck12.org Chapter 7. Vectors
7.4 Dot Product and Angle Between Two Vec-
tors
Here you will compute the dot product between two vectors and interpret its meaning.
While two vectors cannot be strictly multiplied like numbers can, there are two different ways to find the product
between two vectors. The cross product between two vectors results in a new vector perpendicular to the other two
vectors. You can study more about the cross product between two vectors when you take Linear Algebra. The
second type of product is the dot product between two vectors which results in a regular number. This number
representshow much of one vector goes in the direction of the other. In one sense, it indicates how much the two
vectors agree with each other. This concept will focus on the dot product between two vectors.
What is the dot product between<− 1 , 1 >and< 4 , 4 >? What does the result mean?
Watch This
Watch the portion of this video focusing on the dot product:
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61368http://www.youtube.com/watch?v=EYIxFJXoUvA James Sousa: Vector Operations
Guidance
The dot product is defined as:
u·v=<u 1 ,u 2 >·<v 1 ,v 2 >=u 1 v 1 +u 2 v 2
This procedure states that you multiply the corresponding values and then sum the resulting products. It can work
with vectors that are more than two dimensions in the same way.
Before trying this procedure with specific numbers, look at the following pairs of vectors and relative estimates of
their dot product.