I want to proof that, given vector a non zero and a vector b, so
I know how to proof <=
but how to proof =>?
My try:
I tried to prove
Now
so b is orthogonal to both a and c
so
So if we have my doubt is, my I affirm this???
Plato post #2 is correct. But define, out of the clear blue sky?
axb is perpendicular to a and b and (axb)xa is then in direction b.
(axb)xc=(a.c)b - (a.b)c from vector algebra, look it up.
(axb)xa=(a.a)b - (a.b)c, which gives Plato's formula, c=axb/a^{2}