E-Storevectors-quick see.(II)
Vector Product
DEFINITION : The vector product is fundamentally different from the scalar product. The vector product of two vectors is a vector but the scalar product is a scalar. The vector product is given by:
where
|a| = is the length of a or b
&theta = is the angle between vectors
n = is the unit vector perpendicular to a and b whose direction is determined by the left hand skew rule.
For vectors a x b is found by using the following:
For simplicity this can be written in terms of determinants
Now try the vector product yourself
DEFINITION :In terms of vectors the area of the triangle below is: source=internet.
The Area of a Vector Triangle
Try finding the area of your own vector triangles
Recall that the vector equation of a plane is ( r - a ) . n = 0 where a is a point on the plane and n is a vector normal to the plane.
Say if we have points 
which are in Cartesian form. We firstly need to find the vector parallel to the plane.
To get a vector n, which is normal to the plane, we take the vector product of the above vectors.
This gives a vector denoted n by So the equation of the plane is found using the same method as above
By substituting in we get 
Find the equation of your plane given three of your own points
DEFINITION : Skew lines are lines or vectors which are not parallel and do not meet. We now seek the minimum distance between these lines By drawing a line between both lines: called a transversal it will be perpendicular to both lines. 
The transversal connects A and B and n3 is the unit vector in the direction AB and p is the required distance.
As mentioned above n3 is perpendicular to both n1 and n2
Finding the Equation of a Plane given Three Points
Minimum distance between two skew lines
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