Question

How do i show this? \[\left( a X b \right) Dot b = 0\] for all vectors a and b in V3

Answer 1

maybe we can do something with this
i haven't decided yet

Answer 2

and then we can write
x(bz-yc+y^2-zb)+y(-az+az)=0 if i didn't make a mistake
x(-yc+y^2)+y(0)=0
x(-yc+y^2)=0
xy(y-c)=0

Answer 3

x=0, y=0, y=c (this should imply c=0 since y=0)

Answer 4

so we have vector A=<a,b,0> and B=<0,0,z>
what do you think?

Answer 5

anything in this form as long as you have x=y=c=0

Answer 6

i think i like this problem