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Dot product = Sum (xi*yi), i=0..n
- Eila June 11, 2006Cross product = matrix determinant (http://en.wikipedia.org/wiki/Cross_product)
from site: http://members.tripod.com/~Paul_Kirby/vector/Vplane.html
a plane formula is calculated by its normal:
Let a, b, c be the position vectors of 3 points in the plane. Then all we have to do to find the equation of the plane is construct a normal vector - then we can use this and any of the 3 points to find the equation as before.
The two vectors,
b - a (A to B)
c - a (A to C)
both lie in the plane, so if we take their cross product we find our normal vector:
n = (b - a) x (c - a) => cross product
the distance between the plane and the point is:
from :http://www-math.mit.edu/~djk/18_022/chapter02/example01.html
lets set p to be a point in the space, than:
((p-a),n)/(n,n)
Form the vector p - a and take its dot product with n divided by the magnitude of n.
The magnitude of the result will be the required distance.