Which act would NOT bind the partnership if conducted by a partner without proper authority?

In a partnership, the general rule is that partners have authority to bind the partnership in dealings that are within the scope of the partnership's business. However, if a partner acts outside the scope of their authority or engages in a transaction that is not typical of the partnership's activities, those actions may not bind the partnership.

In the context of the choices, purchasing supplies for the partnership, negotiating deals, and selling products are typically actions that fall within a partner's authority and would thus bind the partnership. These activities are considered part of normal business operations.

On the other hand, the act of buying a vehicle could be classified as outside the ordinary scope of business operations for many partnerships. If the partnership does not ordinarily engage in purchasing vehicles, and the partner does so without proper authority, this action would not bind the partnership. This is because it is not a transaction typically associated with running a partnership, suggesting that the partner lacked the authority to conduct this specific type of transaction on behalf of the partnership.

Therefore, the selection aligns with the principle that partners must generally act within their authority and in the normal course of the partnership's business for their actions to bind the partnership effectively.