Let H Be the Hyperplane Through the Points A) $f \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) = x _ { 1 } + x _ { 2 } + \frac { 5 } { 2 } x _ { 3 } , d = \frac { 9 } { 2 }$

Multiple Choice

Let H be the hyperplane through the points. Find a linear functional f and a real number d such that H = [f : d].
- $\left[ \begin{array} { l } 1 \\ 1 \\ 1 \end{array} \right] , \left[ \begin{array} { r } 3 \\ - 1 \\ 5 \end{array} \right] , \left[ \begin{array} { r } 4 \\ 2 \\ - 2 \end{array} \right]$

A) $f \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) = x _ { 1 } + x _ { 2 } + \frac { 5 } { 2 } x _ { 3 } , d = \frac { 9 } { 2 }$
B) $f \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) = - 2 x _ { 1 } + 9 x _ { 2 } + x _ { 3 } , d = 8$
C) $f \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) = 8 x _ { 1 } + 2 x _ { 2 } + 4 x _ { 3 } , d = 14$
D) $f \left( x _ { 1 } , x _ { 2 } , x _ { 3 } \right) = x _ { 1 } + 9 x _ { 2 } + 4 x _ { 3 } , d = 14$