Solving For Two Vectors With a Given Dot and Cross Product
we can solve these equations by first taking the dot product of (1) wuthto give
The left hand side of this equation equals zero sinceis perpendicular toso
Now use the identity
Henceandare multiples of each other or
Ifandare multiples of each other, from (1)andare pendicular so both are 0 then from (2),is arbitrary.
Ifthen from (1),andare parallel so