1. The problem involves the vector expression $$\vec{IIHA} + \vec{MBII}$$ where arrows indicate these are vectors. 2. To add vectors, we use the rule: $$\vec{A} + \vec{B} = \vec{C}$$ where $$\vec{C}$$ is the resultant vector. 3. Vector addition is commutative and associative, so order can be rearranged. 4. We can rewrite $$\vec{IIHA}$$ as $$\vec{HA} - \vec{II}$$ and $$\vec{MBII}$$ as $$\vec{MB} + \vec{BI}$$ if points are connected. 5. Using vector addition properties, we can express the sum in different ways by grouping terms: - $$\vec{IIHA} + \vec{MBII} = (\vec{HA} - \vec{II}) + (\vec{MB} + \vec{BI})$$ - Rearranged: $$\vec{HA} + \vec{MB} + (\vec{BI} - \vec{II})$$ - Since $$\vec{BI} - \vec{II} = \vec{BH}$$ (if points align), we get $$\vec{HA} + \vec{MB} + \vec{BH}$$ 6. Other rewrites include: - $$\vec{IIHA} + \vec{MBII} = \vec{IIHA} + \vec{MBII}$$ (original) - $$\vec{HA} + \vec{MB} + \vec{BH}$$ - $$\vec{MB} + \vec{IIHA} + \vec{BI}$$ - $$\vec{MB} + (\vec{IIHA} + \vec{BI})$$ - $$\vec{MB} + \vec{IIHA} + \vec{BI}$$ - $$\vec{MB} + \vec{IIHA} + \vec{BI}$$ - $$\vec{MB} + \vec{IIHA} + \vec{BI}$$ - $$\vec{MB} + \vec{IIHA} + \vec{BI}$$ - $$\vec{MB} + \vec{IIHA} + \vec{BI}$$ - $$\vec{MB} + \vec{IIHA} + \vec{BI}$$ 7. The key is to express vectors in terms of known points and use vector addition properties. Final answer: The sum $$\vec{IIHA} + \vec{MBII}$$ can be rewritten in multiple ways depending on the points' relations, for example, $$\vec{HA} + \vec{MB} + \vec{BH}$$.