Provide an Appropriate Response $S$ Of Four Distinct Points In $R ^ { 3 }$

question 24

Multiple Choice

Provide an appropriate response.
-Pick a set $S$ of four distinct points in $R ^ { 3 }$ such that aff $S$ is the plane $2 x _ { 1 } + x _ { 2 } - 3 x _ { 3 } = 14$ .

• A) \(\mathrm { S } = \left\{ \left[ \begin{array} { r } 2 \\ 1 \\ - 3 \end{array} \right] , \left[ \begin{array} { r } 4 \\ 2 \\ - 6 \end{array} \right] , \left[ \begin{array} { r } 0 \\ 14 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 15 \\ 1 \end{array} \right] \right\}\)
• B) \(\mathrm { S } = \left\{ \left[ \begin{array} { r } 0 \\ 17 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 1 \\ 9 \\ - 1 \end{array} \right] , \left[ \begin{array} { r } - 2 \\ 18 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 0 \\ 14 \\ 0 \end{array} \right] \right\}\)
• C) \(\mathrm { S } = \left\{ \left[ \begin{array} { r } 2 \\ 15 \\ 1 \end{array} \right] , \left[ \begin{array} { r } - 1 \\ 9 \\ - 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ 10 \\ 0 \end{array} \right] , \left[ \begin{array} { l } 0 \\ 0 \\ 0 \end{array} \right] \right\}\)
• D) \(\mathrm { S } = \left\{ \left[ \begin{array} { r } 0 \\ 11 \\ 1 \end{array} \right] , \left[ \begin{array} { l } 1 \\ 9 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 2 \\ 18 \\ 0 \end{array} \right] , \left[ \begin{array} { r } 0 \\ 14 \\ 0 \end{array} \right] \right\}\)