Finding the angle between vectors.

[Rumor]

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 AP and PB and then taking the dot product between the two to find the angle.

For AP, I got AP = 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?

 

[tkhunny]

Couple of things.

1) Does the dot product give the angle? Are you sure it's not hte cosine of the angle?
2) A[1] = P[1]. How did you get PA[1] = 1 rather than zero (0)?