Trong không gian Oxyz, cho mặt cầu 

A

- Hướng dẫn giải

\(\begin{array}{l}\left( P \right) \bot \Delta \Leftrightarrow \overrightarrow {{n_P}} = \overrightarrow {{u_d}} = \left( {2; - 2;1} \right)\\ \Rightarrow \left( P \right):2\left( {x - {x_0}} \right) - 2\left( {y - {y_0}} \right) + \left( {z - {z_0} = 0} \right)\\\left( S \right):{\left( {x - 1} \right)^2} + {\left( {y + 2} \right)^2} + {\left( {z - 1} \right)^2} = 9\\ \Rightarrow I\left( {1; - 2;1} \right);R = 3\end{array}\)

(P) tiếp xúc (S) khi: \({d_{\left( {I,\left( P \right)} \right)}} = 3\)

\(\begin{array}{l} \Leftrightarrow \frac{{\left| {2\left( {1 - {x_0}} \right) - 2\left( { - 2 - {y_0}} \right) + \left( {1 - {z_0}} \right)} \right|}}{{\sqrt {{2^2} + {2^2} + {1^2}} }} = 3\\ \Leftrightarrow \left| {2{x_0} - 2{y_0} + {z_0} - 7} \right| = 9\end{array}\)