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This node uses standard vector/matrix mathematics. Say we have two input vectors, (a,b,c) and (d,e,f), and we are calculating the output vector (x, y, z). The calculations are defined as follows:
Dot Product is defined as follows:
Dot Product = (a*d) + (b*e) + (c*f)A dot product is a single value, so all three output values x, y and z will be set to the same thing.
The Cross Product of two vectors gives you a new vector. This new vector is guaranteed to be perpendicular (i.e. at right angles to) both of the input vectors.
Cross Product is defined as follows:
x = (b*f)(c*e)
y = (c*d)(a*f)
z = (a*e)(b*d)
Note: If you just want to do simple componentbycomponent combinations of your vectors (i.e., x = a*d, y=b*e, z=c*f) then you should use the Multiply Divide utility node instead of the Vector Product utility node.
The Vector Matrix Product is useful for taking a vector in one coordinate space and moving it to another. For example, if you have a vector in camera coordinate space, you can multiply it by the Xform Matrix attribute of the camera. That will give you a new vector in world coordinate space.
Similarly, the Point Matrix Product is useful for taking a point in one coordinate space and moving it to another. For example, if you have a point in camera coordinate space, you can multiply it by the Xform Matrix attribute of the camera. That will give you a new point in world coordinate space.
Given an input vector (a, b, c) and an input matrix:
A B C D E F G H I J K L M N O P
Then Vector Matrix Product is defined as follows:
x = (a*A) + (b*B) + (c*C) y = (a*E) + (b*F) + (c*G) z = (a*I) + (b*J) + (c*K)And the Point Matrix Product is defined as follows:
x = (a*A) + (b*B) + (c*C) + D y = (a*E) + (b*F) + (c*G) + H z = (a*I) + (b*J) + (c*K) + L
In the table below, important attributes have their names listed in bold in the description column.
This node is MP safe
Node name  Parents  Classification  MFn type  Compatible function sets 

vectorProduct  shadingDependNode  utility/general:drawdb/shader/operation/vectorProduct  kVectorProduct  kBase kNamedObject kDependencyNode kVectorProduct 
plusMinusAverage, reverse, chooser, choice, blend, blendTwoAttr, blendWeighted, blendDevice
input1, input1X, input1Y, input1Z, input2, input2X, input2Y, input2Z, matrix, normalizeOutput, operation, output, outputX, outputY, outputZ
Long name (short name)  Type  Default  Flags  

operation
(op )
 enum  1  
 
input1
(i1 )
 float3  0.0, 0.0, 0.0  
 
 
 
input2
(i2 )
 float3  0.0, 0.0, 0.0  
 
 
 
matrix
(m )
 fltMatrix  identity  
 
normalizeOutput
(no )
 bool  false  
 
output
(o )
 float3  1.0, 0.0, 0.0  
 
 
