Just how the cross product between two vectors yields the area of a parallelogram, when adding a third dimension, the geometric interpretation of a triple cross product would be the volume of a parallelepiped.
bean
Because all three terms are crossing the same norm vectors together, the magnitude of each term is the same. Each of the cross products between any two of w, u, v will be pointing up. The third cross product causes all of the vectors to be facing perpendicularly outward from w, u, v, respectively. Since the three sides altitudes meet at a point, the second cross product in each term will emerge from the same point. Since they all have the same magnitude, the terms cancel
yumz
I learned to memorize Lagrange's identity as ABC = BAC - CAB
Just how the cross product between two vectors yields the area of a parallelogram, when adding a third dimension, the geometric interpretation of a triple cross product would be the volume of a parallelepiped.
Because all three terms are crossing the same norm vectors together, the magnitude of each term is the same. Each of the cross products between any two of w, u, v will be pointing up. The third cross product causes all of the vectors to be facing perpendicularly outward from w, u, v, respectively. Since the three sides altitudes meet at a point, the second cross product in each term will emerge from the same point. Since they all have the same magnitude, the terms cancel
I learned to memorize Lagrange's identity as ABC = BAC - CAB