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

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- November 2nd 2008, 12:42 PMmonkiusVectors
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 - November 2nd 2008, 01:00 PMskeeter
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. - November 2nd 2008, 01:05 PMPlato

Applying these two will answer your question. - November 3rd 2008, 03:55 AMHallsofIvy
It also helps to know that , the "triple product", can be written in the determinant form:

In the case of either or , two of the rows of the determinant are the same and so the determinant is 0.