For starters, vectors are always joined head-to-tail. So you should really be finding the angles between and , not . But that's just a scaling factor of .
So, given that A = (1,0,0), B = (2,0,0) and P = (1, -(1/sqrt(3)), -(sqrt(2/3))), find the angle APB.
I've started on this problem by choosing to use the vectors PA and PB and then taking the dot product between the two to find the angle.
For PA, I got PA = -i - 1/sqrt(3) - sqrt(2/3)k.
and for PB, I got PB = i - 1/sqrt(3)j - sqrt(2/3)k.
And for the dot product and angle, I get 0, which can't be right. Could someone help me out?