Vector Algebra

Between the following two statements:

Statement I : Let \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-\hat{k}\). Then the vector \(\vec{r}\) satisfying \(\vec{a} \times \vec{r}=\vec{a} \times \vec{b}\) and \(\vec{a} \cdot \vec{r}=0\) is of magnitude \(\sqrt{10}\).

Statement II : In a triangle \(A B C, \cos 2 A+\cos 2 B+\cos 2 C \geq-\frac{3}{2}\).