Cross Product
These are two vectors:
They can be multiplied using the "Cross Product"
(also see Dot Product).
The Cross Product a × b of two vectors is another vector that is at right angles to both:
And it all happens in 3 dimensions!
Calculating
You can calculate the Cross Product this way:
a × b = a b sin(θ) n a is the magnitude (length) of vector a b is the magnitude (length) of vector b θ is the angle between a and b n is the unit vector at right angles to both a and b So the length is: the length of a times the length of b times the sine of the angle between a and b, Then you multiply by the vector n to make sure it heads in the right direction. 
OR you can calculate it this way:
When a and b start at the origin point (0,0,0), the Cross Product will end at:

They both work!
Example: What is the cross product of a = (2,3,4) and b = (5,6,7)
 c_{x} = a_{y}b_{z}  a_{z}b_{y} = 3×7  4×6 = 3
 c_{y} = a_{z}b_{x}  a_{x}b_{z} = 4×5  2×7 = 6
 c_{z} = a_{x}b_{y}  a_{y}b_{x} = 2×6  3×5 = 3
Answer: a × b = (3,6,3)
Which Way?
The cross product could point in the completely opposite direction and still be at right angles to the two other vectors, so we have the:
"Right Hand Rule"
With your righthand, point your index finger along vector a, and point your middle finger along vector b: the cross product goes in the direction of your thumb.
Dot Product
The Cross Product gives a vector answer, and is sometimes called the "vector product"
But there is also the Dot Product which gives a scalar (ordinary number) as an answer.
Question: What do you get when you cross an elephant with a banana? Answer: elephant banana sin(θ) n 