$$\vec{u} \cdot \vec{v} = |\vec{u}| |\vec{v}| \cos\theta = u_1v_1 + u_2v_2 + u_3v_3$$

$$\rightarrow \cos\theta = \frac{\sum_{n=1}^{3} u_n v_n}{|\vec{u}| |\vec{v}|}$$

So, first calculate:

$$|\vec{u}| = (1^2 + (-1)^2 + 0^2)^{1/2} = \sqrt{2}$$ $$\& \quad |\vec{v}| = (2^2 + 1^2 + 2^2)^{1/2} = \sqrt{9} = 3$$

Then:

$$\sum u_n v_n = 1(2) + (-1)(1) + 0(2) = 2 - 1 = 1$$

Finally:

$$\cos\theta = \frac{1}{(\sqrt{2})(3)} \approx 0.2357$$

$$\theta = \cos^{-1}(0.2357) = 76.4° \approx 1.33 \text{ rad}$$