Find the orthogonal projection of (x,y,z) onto the subspace of R^3 spanned by vectors (1,2,2),(-2,2,-1).
what i did was
[(x,y,z).(1,2,2)](1,2,2) + [(x,y,z).(-2,2,-1)](-2,2,-1)
which is equals to
(x+2y+2z,2x+4y+4z,2x+4y+4z) + (4x-4y+2z,-4x+4y-2z,2x-2y+z)
and then that is equals to
but the answer given is 1/9(5x-2y+4z,-2x+8y+2z,4x+2y+5z)
which is the same as what i got except the 1/9 in front. can anyone tell me what i did wrong?
if i am given 2 vectors X & Y in R^3 and given the inner product of <X,Y>
how do i calculate the angle between X and Y? i know how to calculate ||X|| and ||Y|| which is just <X,X> and <Y,Y> right?