csat-suneung· South-Korea· csat__math-science4 marks
In coordinate space, the figure $S$ is formed by the intersection of the sphere $( x - 1 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z - 1 ) ^ { 2 } = 9$ with center C and the plane $x + y + z = 6$. For two points $\mathrm { P } , \mathrm { Q }$ on figure $S$, what is the minimum value of the dot product $\overrightarrow { \mathrm { CP } } \cdot \overrightarrow { \mathrm { CQ } }$ of the two vectors $\overrightarrow { \mathrm { CP } } , \overrightarrow { \mathrm { CQ } }$? [4 points] (1) - 3 (2) - 2 (3) - 1 (4) 1 (5) 2
In coordinate space, the figure $S$ is formed by the intersection of the sphere $( x - 1 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + ( z - 1 ) ^ { 2 } = 9$ with center C and the plane $x + y + z = 6$.\\
For two points $\mathrm { P } , \mathrm { Q }$ on figure $S$, what is the minimum value of the dot product $\overrightarrow { \mathrm { CP } } \cdot \overrightarrow { \mathrm { CQ } }$ of the two vectors $\overrightarrow { \mathrm { CP } } , \overrightarrow { \mathrm { CQ } }$? [4 points]\\
(1) - 3\\
(2) - 2\\
(3) - 1\\
(4) 1\\
(5) 2