Calculating Angle of Deviation when Building Tilted on Plane

[doublemint]

Homework Statement

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?

Homework Equations

Dot Product
Cross Product

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 don't 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 don't know what the answer is, I'm using webwork
So if anyone can help me, that would be great.

Thanks

 

[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).

 

[doublemint]

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