If you read ALL of the article, you will see that the author DOES discuss the reasons why you should NOT use these methods indiscriminately. In the course of doing LEGITIMATE work, many of us MUST use tricks to get around IT department security restrictions. For example, ALL HTML documents and ALL .ZIP files are blocked by our EMail server. We often need to send reports in HTML format to other people and send .ZIP files containing various types of other information. To do this, we have to change the file extension of the attachment. (Equivalent to smuggling AK-47s by putting them in a box labeled "shovels".) This article DOES discuss the risks associated with circumventing security (divulging confidential information, computer infection with viruses and other malware, etc.) Until IT department security policies become 100% based on reason, people who actually want to get their work done NEED to find ways to work around them WHEN NECESSARY. (NOT just to play games during work hours!)

John Morgan Center for Health Statistics Arkansas Department of Health and Human Services

The cross product of two vectors A and B is a third vector (A x B) that is perpendicular to BOTH A and B. The magnitude of (A x B) is equal to the product of the magnitudes of the first two vectors and the sine of the angle between A and B: |A x B| = |A| |B| sin(/_ A,B) The perpendicularity condition determines the (two-headed) line in the direction of (A x B). The magnitude condition narrows down (A x B) to one of two vectors. The precise choice of (A x B) follows the right hand rule: 1.) Point your RIGHT index finger along A. 2.) Point your RIGHT middle finger along B. 3.) Lift your RIGHT thumb perpendicular to the plane of your index and middle fingers. It will then point along (A x B). (If you use your LEFT hand, you will get -(A x B) NOT (A x B). Whether to use a RIGHT hand rule or a LEFT hand rule is essentially just an arbitrary choice, but it needs to be used consistently. The right hand rule for moving currents and magnetic field in electricity basically come from the right hand rule for cross products.) The origin of the cross product actually comes from looking at tensor products: If A = A1 i + A2 j + A3 k and B = B1 i + B2 j + B3 k then AB = A1*B1*i*i + A1*B2*i*j + ... + A3*B2*k*j + A3*B3*k*k where i, j, and k are unit vectors in the X, Y, and Z directions, respectively. (The tensor product is usually represented as a square matrix.) The dot product is the trace (the sum of the ii part, the jj part, and the kk part) and the cross product is the antisymmetric part of the tensor product. The i component of (A x B) is the jk component of the tensor minus the kj component, etc. In matrix terms, look at AB - BA: The diagonal terms are all zero, the off-diagonal terms are the components of (A x B). As to when you would use it? It depends on how often you need to find a line perpendicular to two other lines. John Morgan Center for Health Statistics Arkansas Department of Health and Human Services