# Vector Problem

1. Nov 7, 2009

### doublemint

1. The problem statement, all variables and given/known data

A vertical building was built on a horizontal plane. The plane is then tilted to A=(0,0,0) B=(1,2,0) and C=(0,3,1). By what angle (in radians) does the building now deviate from the vertical?

2. Relevant equations

Dot Product
Cross Product

3. The attempt at a solution

So what I did was take the cross product of the B and C, relative to A.

BxC = |2 0|, |1 0|, |1 2| = (2, -1, 3)
........|3 1|, -|0 1|, |0 3|

Now this is the part where I dont know what to do.

I took the Dot product of (BxC) with (0, 1, 0)

theta = arccos (u.v)/(|u||v|) = (-1/$$\sqrt{}14$$$$\sqrt{}1$$)

and i got an angle to be 1.84 in radians, which was wrong. I dont know what the answer is, I'm using webwork
So if anyone can help me, that would be great.

Thanks

2. Nov 7, 2009

### Dick

Why do you think the vertical direction is (0,1,0)? My guess would have been that they meant it to be (0,0,1).

3. Nov 8, 2009

### doublemint

Your Right! I must of been thinking in 2D..
Thank You Dick!!