Find the smaller angle between vectors a and b a= b=

Question

Find the smaller angle between vectors a and b a= <3,2,1> b=<-3,0,-1>

anonymous · Answer

so this is what i have so far, and i'm not sure if i did it correctly or not...
aob = ||a|| ||b|| CosTheta
-10 = $$-10= \sqrt(14)\sqrt(10) Cos \theta$$

anonymous · Answer

so i get 
$$\cos \theta = -10/ 11.8$$

anonymous · Answer

if i arctan this i get 32.4, but apparently that's not the right answer? o.O

anonymous · Answer

i mean, arc cos lol

anonymous · Answer

yes.you are right.

anonymous · Answer

my teacher marked it wrong :( i think i may have done something wrong somewhere? o.O

cwrw238 · Answer

i got 32.06 degrees

anonymous · Answer

i think you may have done some calc. mistakes

anonymous · Answer

wait, i got 32.06 on my calculator lol but marked down 32.4
would she seriously mark me off 3 points because i'm off .34 points..???

cwrw238 · Answer

wait isnt aob = -8 ?  
no - forget that -10 is right

cwrw238 · Answer

yea 32.06 is correct

cwrw238 · Answer

3 points off is a bit harsh - marks are usually awarded for method and accuracy and you had the method right

anonymous · Answer

is it the smaller of the two angles? maybe that's why it's wrong? is it possible to have a smaller angle?

anonymous · Answer

no.the other one is 
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