I am posting a multipart question it has 6 parts that need t

I am posting a multipart question, it has 6 parts that need to answered (A through G, but C does not need to be worked out), some much easier than others. The questions are connected to the other, so I\'m not sure how else to post them :/. I\'ll be making 5 different posts so that you get the credit for all the work put it. (I\'ll be posting all the links to all 5 posts in everyone of the questions so you can find them easily)

Just in case, this might look like a lot more work than it actually is bc my prof is wordy.

Solution

e) Let cx d = e where e is a vector

Then left side

= (axb).e

= b.(exa) (using scalar triple property)

= b.{(cxd) xa}

= b.{(a.c)d-c(a.d)} (Using vector triple product inside the bracket)

= (a.c).(b.d) - (b.c)(a.d)

Since a.c is a scalar taken out and dot product is with b outside.