- #1
cordines
- 15
- 0
i) Show that: a x ( b x c) + b x ( c x a) + c x (a x b ) =0
I managed to this, by expanding each term using the definition of the triple vector product i.e. a x ( b x c) = (a.c)b-(a.b)c and adding the results.
ii) and deduce that
a x { b x ( c x d ) } + b x { c x ( d x a ) } + c x { d x ( a x b) } + d x { a x ( b x c ) } =
( a x c ) x ( b x d)
I expanded each term like i did in the first an added the results an obtained:
-(d x b)(b.a) - (d.a)(c x b) - (b x a)(c.d) - (b.c)(a x d )
Clearly the result does not agree, and I can't find any means how to simplify it. Some help anyone? Thanks
I managed to this, by expanding each term using the definition of the triple vector product i.e. a x ( b x c) = (a.c)b-(a.b)c and adding the results.
ii) and deduce that
a x { b x ( c x d ) } + b x { c x ( d x a ) } + c x { d x ( a x b) } + d x { a x ( b x c ) } =
( a x c ) x ( b x d)
I expanded each term like i did in the first an added the results an obtained:
-(d x b)(b.a) - (d.a)(c x b) - (b x a)(c.d) - (b.c)(a x d )
Clearly the result does not agree, and I can't find any means how to simplify it. Some help anyone? Thanks