basic physics question about vectors

[Hmongkeysauce]

given vector A=-3i-2j+6k and vector B=12i-3j+4k
find the angel between them using:
1)the dot product rule
2)the cross product rule

for verification purposes:
A*B=-6
AxB=10i-84j+33k
and |AxB|=90.8

therefore, if s=angle between the two vectors:
1)-6=|A||B|cos(s); s=93.8
2)90.8=|A||B|sin(s); s=86.2

question is, why are they NOT the same angle? and if not the same, then, which method should be used to find the angle between two vectors?

 

[watdahel]

That's an easy one. Yup. I thought it's gonna be harder. Someone will respond with the answer I'm sure.

 

[thepd7]

the cross product is 10i + 84j +33k, not minus in the middle. You forgot that when you do the determinant, there its like this
|+ - +|
|- + -|
|+ - +|

and technically i is top left, j is top middle, k is top right. So thats where the extra negative sign comes from. I am not sure if this fixes it but it probably does.



edit: was right about the above but it doesn't change anything, still working

 

[thepd7]

still not 100% sure and its late, but I know that if the dot product is 6 instead of -6 they are the same angle and that the 2 angles you got (same answer as me) are complimentary, they add to 180 degrees. So could be thats right? not sure, I am going to bed.