acos and the angle between vectors



Hello

I am trying to figure the angle between vector and
getting some un-expected answers

(%i114) magnitude(x) := sqrt(x.x)$

(%i115) a:[1,0]$ b:[0,1]$ c:[1,2]$
d:[sqrt(2),sqrt(7)]$

(%i119) acos((a.b)/(magnitude(a)*magnitude(b)));
(%o119) %pi/2	 <---- expected
		
(%i120) acos((c.d)/(magnitude(c)*magnitude(d)));

(%i122) acos((c.d)/(magnitude(c)*magnitude(d)));
(%o122) acos((2*sqrt(7)+sqrt(2))/(3*sqrt(5))) <--
pi/??

does it need to be hand written in-order to get a
answer?


(%i124) e:2*sqrt(7) + sqrt(2) ,numer;
(%o125) 6.705716184502276

(%i126) 3*sqrt(5) ,numer;
(%o126) 6.708203932499369

(%i127) acos(%o125/%o126);
(%o127) 0.0272350692885    <--- even now, where is the
radians answer


thanks





	
		
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