How Do Vector Components Relate in Orthogonal Projections and Cross Products?

[iric]

104. If a, b, c and a’, b’, c’ are such that
a’• a = b’• b = c’• c = 1
a’• b = a’• c = b’• a = b’• c = c’• a = c’ • b =0

Prove that it necessarily follows that
a^'= (b x c)/(a• bxc) , b^'= cxa/(a•bxc) ,
c^'= axb/(a•bxc)

 

[magwas]

Try to figure out the direction of a' with respect to b and c. What will be the direction of bxc with respect to a'?
Now figure out the length of bxc using |a|, |a'| and the angle between a and a',