hi this is about vector calculus subscript notation:
i generally understand v.c.s.n but can't do something like this:
Show : (AXB) . (CXD) = (A.C)(B.D) - (A.D)(B.C)
my work so far:
so (AXB) . (CXD) =
=
=
=
=
=(A.C)(B.D) - (B.D)(A.C)
the first part of the answer (in red) i got right.. but the 2nd part is wrong as you can see
how am i meant to get -(A.D)(B.C)???
thanks guys please help out
cheers dan, your method is easy to understand. it's frustrating trying to learn all this calculus on your own when there is just a huge pile of books and you're forever researching. so i appreciate your help.
just a question though, on the 2nd epsilon identity you used:
what i wanted to ask is: do you have to use the imn notation.. or can you use any preferred notation.. such as ixy....
i understand the final result will still be the same as long as the notation is consistent throughout the solution, but i just wanted to confirm whether imn has to be used as a standard for vector calculus. thanks once again .
You can use any indices you like. (You can even make up your own, but they're much harder to type. ) The point is that they are different from the ones you used previously since they have no relation to the indices in the other cross product.
By the way, a nice way to remember that epsilon-epsilon identity:
Note that the "i" index doesn't appear anywhere in the deltas. Now look at the first delta of each pair. They both have a "j," the first index after the "i" in the first epsilon. The second index of those first deltas is in sequence, m and n... the second and third indices of the second epsilon.
-Dan