Vector3D.project() method in [Help] of Flash CS4 Professional says:

If the current Vector3D object is the result of multiplying a Vector3D object by a projection Matrix3D object, the w property can hold the transform value.

However a Vector3D.w property does not hold its original value. I suppose that the method for multiplication is the Matrix3D.transformVector(). Then see the result of the following script:

var myMatrix3D:Matrix3D = new Matrix3D();
var myVector3D:Vector3D = new Vector3D();
trace(myVector3D, myVector3D.w);  // Output: Vector3D(0, 0, 0) 0
myVector3D = myMatrix3D.transformVector(myVector3D);
trace(myVector3D, myVector3D.w);  // Output: Vector3D(0, 0, 0) 1

The default value of the Vector3D.w property is 0. But it is changed into 1 as the result of multiplication. The property does not hold the original value. No number multiplied by 0 can result to 1.

On the other hand, the Vector3D.add() and the Vector3D.subtract() methods reset Vector3D.w property to 0. The property is ignored by these methods.

While the Matrix3D.transformVector() method set the Vector3D.w property's value of the multiplying Vector3D instance to 1, the method does not ignore the property but multiplies it by the Matrix3D instance.

The code below creates a Matrix3D instance, of which the fourth row is set to [4, 3, 2, 5]. The result value of the Vector3D.w property after multiplication is 34. The value is the dot product of the multiplying Vector3D instance (whose Vector3D.w property is 1) and the fourth row of Matrix3D instance.

(4, 3, 2, 5)•(4, 3, 2, 1) = 4x4 + 3x3 + 2x2 + 5x1 = 34

Multiplying a Vector3D by a Matrix3D

var myMatrix3D:Matrix3D = new Matrix3D();
var myRawData:Vector.<Number> = myMatrix3D.rawData;
var myVector3D:Vector3D = new Vector3D(4,3,2);
trace(myVector3D, myVector3D.w);  // Output: Vector3D(4, 3, 2) 0
myRawData[3] = 4;
myRawData[7] = 3;
myRawData[11] = 2;
myRawData[15] = 5;
myMatrix3D.rawData = myRawData;
myVector3D = myMatrix3D.transformVector(myVector3D);
trace(myVector3D, myVector3D.w);  // Output: Vector3D(4, 3, 2) 34

I assume that the sentence in the [Help] quoted in this article implies this process. But it is hard to understand from the expression especially for non-english speaking people. At least it should be mentioned that the Vector3D.w property's value of the multiplying Vector3D instance is set to 1.