The discussion centers on the significance of the order of operations when using the triple scalar product in vector calculus. It is established that the cross product is anti-symmetric, meaning that changing the order of the vectors affects the sign of the result but not the magnitude. Specifically, the expressions \bullet c and \bullet b yield results that differ only by a sign, confirming that the order of the vectors is crucial in determining the outcome.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are working with vector calculus and need to understand the implications of vector operations on volume calculations.
Yes, it matters, because the cross product is anti-symmetric.e^(i Pi)+1=0 said:Of the 3 vectors, does it matter what order I cross / dot them?
<a [itex]\times[/itex] b> [itex]\bullet[/itex] c =? <a [itex]\times[/itex] c> [itex]\bullet[/itex] b