justift whether ( u+v)dot(u cross v)=0 for all non-zero vectors u and v.
need help with this question, managed to finish rest in problem set. thanks for the help
let u = ai + bj + ck
v = di + ej + fk
u + v = (a+d)i + (b+e)j + (c+f)k
u X v = (bf - ce)i - (af - cd)j + (ae - bd)k
(u + v) dot (u X v) =
(a + d)(bf - ce) - (b + e)(af - cd) + (c + f)(ae - bd)
(abf + bdf - ace - cde) - (abf + aef - bcd - cde) + (ace + aef - bcd - bdf)
abf + bdf - ace - cde - abf - aef + bcd + cde + ace + aef - bcd - bdf
believe all these cancel out to 0.