Let $$G$$ be the centroid of a $$\triangle A B C$$ and $$\mathrm{O}_{b_\theta}$$ other point in that plane, then $$\mathrm{OA}+\mathrm{OB}+\mathrm{OC}+\mathrm{CG}=$$

If the volume of the parallelopiped whose conterminus edges are along the vectors $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ is 12, then the volume of the tetrahedron whose conterminus edges are $$\mathbf{a}+\mathbf{b}, \mathbf{b}+\mathbf{c}$$ and $$c+a$$ is

For any non-zero vectors $$\mathbf{a}$$ and $$\mathbf{b}$$,

If the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+m \hat{\mathbf{k}}$$ are coplanar, then $$m=$$