Help with finding angles between vectors

Question

darkbluechocobo · Answer

Find the angle between the vectors, approximate your answer to the nearest tenth: v = 7i − 2j; w = 2i − 3j

darkbluechocobo · Answer

sqrt(7)^2+(-2)^2=sqrt53
sqrt(2)^2 + (-3)^2= sqrt13

darkbluechocobo · Answer

(7*2)+(-2*-3)
14+6=20

20/sqrt53sqrt13

darkbluechocobo · Answer

cos^-1(20/sqrt53sqrt13

darkbluechocobo · Answer

40.4 degrees I believe is the answer

freckles · Answer

one sec let me check each of your parts dot product was done correctly (check mark) magnitude of both vectors... hmm let me check sqrt(49+4)=sqrt(53) sqrt(4+9)=sqrt(13) (check mark) now you did $$\arccos(\frac{20}{\sqrt{53} \cdot \sqrt{13}})$$ and I get (or my wolfram calculator gets) http://www.wolframalpha.com/input/?i=arccos%2820%2F%28sqrt%2853%29*sqrt%2813%29%29 which is yes approximately 40.4 deg looks beautiful to me

darkbluechocobo · Answer

Yay lel i didnt mess up in any work

freckles · Answer

I gave you a medal for your beautiful most correct work! :)