How to calculate the RGB intensity values at center of face using flat shading? Consider a triangular face of three vertices A(0,2,1), B(3,0,1) and the origin, and the normal vectors at the vertices are nA=(0,0,1), nB=(1,1,0) and nO=(-1,-1,1), respectively. The incident light is white and directional in the direction of L=(0,3,4) and the intensity is 1, the background ambient light intensity is 0.1, and the diffuse reflection coefficients for (red, green, blue) are (0.6,0.7,0.8). No specular light contribution need be considered. 

How do I find the (red, green, blue) intensity values at the centre of the face using flat shading?

Flat Shading:

I = Ia x Ka + Fatt x Il x (Kd x (N x L))

Final intensity = ambient reflection x ambient reflection coefficient + (attenuation x incident light intensity x (diffusive reflection coefficient x (surface normal x Light intensity))

My lecturer told me that because ambient reflection coefficient and attenuation are not given, I can forget about it. Also specular light contribution need not be considered.

The surface normal is: 

A = (0, 2, 1) B = (3, 0, 1) O = (0, 0, 0)

U = A - O = (0, 2, 1) V = B - O = (3, 0, 1)

Surface normal = U x V (cross-product) = (2, 3, -6)

I = 0.1 + (1, 1, 1) x ((0.6, 0.7, 0.8) x ((2, 3, -6) x (0, 3, 4)))

I = 0.1 + (1, 1, 1) x ((0.6, 0.7, 0.8) x (0, 9, -2.4))

I = 0.1 + (1, 1, 1) x (0, 6.3, -1.92)

I = (0.1, 6.4, -1.82) = RGB intensity values

Is this correct?
You shouldn't solve for $\cos^{-1}(\theta)$.

The ambient component is as follows (we are assuming the ambient light is white):
$$ambient\ color = (ambient\ light\ color)(ambient\ intensity)(diffuse\ color) = (1,1,1)(0.1)(0.6,0.7,0.8) = (0.06,0.07,0.08)$$

The diffuse component is as follows:
$$diffuse\ color = (light\ color)(light\ intensity)(diffuse\ color)(\cos(\theta)) = (1,1,1)(1)(0.6,0.7,0.8)(0.8) = (0.48,0.56,0.64)$$

Now we just need to add them up:
$$final\ intensity = (diffuse\ color) + (ambient\ color) = (0.06,0.07,0.08) + (0.48,0.56,0.64) = (0.54,0.63,0.72)$$

For more information, here's a pretty decent summary of various lighting calculations.