Provide an appropriate response.
-$\mathbf { v } _ { 1 } = \left[ \begin{array} { l } 2 \ 2 \ 5 \end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { r } 2 \ 3 \ - 1 \end{array} \right] , \mathbf { v } _ { 3 } = \left[ \begin{array} { l } 2 \ 4 \ 3 \end{array} \right]$ and $S = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \right\}$. Aff $S$ is a plane in $R ^ { 3 }$. Give its equation.
A) $13 x + 14 y = 17$
B) $x = 2$
C) $x + y + z = 0$
D) $6 x + 9 y + 7 z = 0$

Question

Quizplus · Accepted Answer

The vectors $\mathbf{v}_1$, $\mathbf{v}_2$, and $\mathbf{v}_3$ all have the same $x$-component, which is $2$. This means that all points in the set $S$ share the same $x$-coordinate, defining a plane parallel to the $yz$-plane at $x = 2$.

Provide an Appropriate Response And S={v1,v2,v3}S = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \right\}S={v1​,v2​,v3​}

Provide an Appropriate Response And $S = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } \right\}$