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

question 29

Multiple Choice

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 \(\mathbf { n } \cdot \mathbf { v } < 7\).

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