Dot ProductYou are currentlybrowsing as guest. Click here to log in 

The "Dot Product" of two vectors is a scalar number that represents how much of one is in the direction of the other.
The dot product is linear in the lengths of the vectors, so for any scalar $c$ and vectors ${\bf~a}$ and ${\bf~b}$ we have $(c{\bf~a}){.}{\bf~b}=c({\bf~a}{.}{\bf~b})$
The dot product is commutative.
The geometric interpretation is that ${\bf~a}{.}{\bf~b}$ is the product of the lengths of the vectors, times the cosine of the angle between them. This implies that if the vectors are orthogonal then the dot product is zero.
If the vectors are finite dimensional then the dot product is obtained by summing the pointwise products of the coordinates.
So if ${\bf~a}=\left[\begin{matrix}a_1\\a_2\\a_3\end{matrix}\right]$ and ${\bf~b}=\left[\begin{matrix}b_1\\b_2\\b_3\end{matrix}\right]$ then ${\bf~a}{\bf.b}=a_1b_1+a_2b_2+a_3c_3.$
Last change to this page Full Page history Links to this page 
Edit this page (with sufficient authority) Change password 
Recent changes All pages Search 