
Find sin(t) where t is the angle between v and w with, 
> v := i+j; w := i+j+k;
v := i + j w := i + j + k

Here I am assuming that the maple session already knows about linalg and the vectors i,j and k. If you start a clean session without any preloading of anything then you MUST first load the linalg package with "with(linalg):" and then define i,j and k as "i := [1,0,0]" etc... 

First define the length function as, 
> len := vec > sqrt(dotprod(vec,vec)):
and then get sin(t) from the geometric definition of the crossprod, 
> sint := len(crossprod(v,w))/(len(v)*len(w));
1/2 sint := 1/3 3
this corresponds to an angle of, 
> convert(angle(v,w),degrees);
1/2 1/2 arccos(1/3 2 3 ) degrees 180  Pi> evalf(%);
35.26438968 degrees