Provide an Appropriate Response
-Let $\mathrm { H }$ Be the Hyperplane Through the Three Points

Provide an appropriate response
-Let $\mathrm { H }$ be the hyperplane through the three points $\left[ \begin{array} { l } 1 \\ 1 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 3 \\ 3 \\ 2 \end{array} \right] , \left[ \begin{array} { r } 2 \\ 5 \\ - 2 \end{array} \right]$ . Is the point $\mathbf { v } = \left[ \begin{array} { l } 4 \\ 2 \\ 1 \end{array} \right]$ on the same side of $\mathrm { H }$ as the origin? Justify your answer.

A) No, because $\mathbf { n } \cdot \mathbf { v } > 0$ .
B) Yes, because $\mathbf { n } \cdot \mathbf { v } < 3$ .
C) No, because $\mathbf { n } \cdot \mathbf { v } > 3$ .
D) Yes, because $\mathbf { n } \cdot \mathbf { v } < 7$ .