Consider points $O(0,0), A, B, C, D, E, F, G$ on a coordinate plane, where points $B$, $C$ and $D$, $E$ and $F$, $G$ and $A$ are located in the first, second, third, and fourth quadrants respectively. If $\vec{v}$ is a vector on the coordinate plane satisfying $\vec{v} \cdot \overrightarrow{OA} > 0$ and $\vec{v} \cdot \overrightarrow{OB} > 0$, then the dot product of $\vec{v}$ with which of the following vectors must be negative? (1) $\overrightarrow{OC}$ (2) $\overrightarrow{OD}$ (3) $\overrightarrow{OE}$ (4) $\overrightarrow{OF}$ (5) $\overrightarrow{OG}$
Consider points $O(0,0), A, B, C, D, E, F, G$ on a coordinate plane, where points $B$, $C$ and $D$, $E$ and $F$, $G$ and $A$ are located in the first, second, third, and fourth quadrants respectively. If $\vec{v}$ is a vector on the coordinate plane satisfying $\vec{v} \cdot \overrightarrow{OA} > 0$ and $\vec{v} \cdot \overrightarrow{OB} > 0$, then the dot product of $\vec{v}$ with which of the following vectors must be negative?\\
(1) $\overrightarrow{OC}$\\
(2) $\overrightarrow{OD}$\\
(3) $\overrightarrow{OE}$\\
(4) $\overrightarrow{OF}$\\
(5) $\overrightarrow{OG}$