Hỏi đáp về Ôn tập cuối năm - Hình học 12

A. \({\left( {x - 2} \right)^2} + {\left( {y - 1} \right)^2} + {\left( {z - 3} \right)^2} = 44.\)

B. \({\left( {x + 1} \right)^2} + {\left( {y - 3} \right)^2} + {z^2} = 44.\)

C. \({\left( {x + 1} \right)^2} + {\left( {y - 3} \right)^2} + {z^2} = 22.\)

D. \({\left( {x - 2} \right)^2} + {\left( {y - 1} \right)^2} + {\left( {z - 3} \right)^2} = 22.\)

A. \(\overrightarrow {{n_1}}  = \left( {2;6;4} \right).\)

B. \(\overrightarrow {{n_4}}  = \left( {2;6; - 4} \right).\) 

C. \(\overrightarrow {{n_3}}  = \left( {1; - 3; - 2} \right).\)

D. \(\overrightarrow {{n_2}}  = \left( {1; - 3;2} \right).\)

A. \(\overrightarrow {{u_1}}  = \left( { - 7;8;9} \right).\) 

B. \(\overrightarrow {{u_4}}  = \left( {7; - 8; - 9} \right).\)

C. \(\overrightarrow {{u_3}}  = \left( {2;2;3} \right).\)

D. \(\overrightarrow {{u_2}}  = \left( {2; - 2; - 3} \right).\)

A. \(\frac{{19}}{{21}} \cdot \)                                        B. \(\frac{{19\sqrt {21} }}{{21}} \cdot \)

C. \(\frac{{\sqrt {21} }}{{21}} \cdot \)                          D. \(\frac{{21}}{{19}} \cdot \)

A. \(\left( {3;\,3;\, - 1} \right)\).

B. \(\left( { - 1;\,3;\, - 3} \right)\).

C. \(\left( {3;\,1;\,1} \right)\).

D. \(\left( {1;\, - 3;\,3} \right)\).

A. \(S =  - \int\limits_a^b {f\left( x \right)\,{\rm{d}}x} .\)

B. \(S = \left| {\int\limits_a^b {f\left( x \right)\,{\rm{d}}x} } \right|.\)

C. \(S = \int\limits_a^b {\left| {f\left( x \right)} \right|\,{\rm{d}}x} .\)

D. \(S = \int\limits_a^b {\,f\left( x \right){\rm{d}}x} .\)

A. \(P\left( {2;0;3} \right).\)

B. \(N\left( {2; - 4;0} \right).\)

C. \(M\left( {0; - 4;3} \right).\)

D. \(Q\left( {0; - 4;0} \right).\)

A. \(\overrightarrow x  = (1; - 5;7).\)

B. \(\overrightarrow x  = (1;5;7).\)

C. \(\overrightarrow x  = (1;5; - 7).\)

D. \(\overrightarrow x  = (0; - 5;7).\)

A. \(\left\{ \begin{array}{l}x = 2 - 5t\\y = 0\\z =  - 3 + 3t.\end{array} \right.\)

B. \(\left\{ \begin{array}{l}x =  - 5 + 2t\\y = 4\\z = 3 - 3t.\end{array} \right.\)

C. \(\left\{ \begin{array}{l}x = 2 + 5t\\y = 4t\\z =  - 3 + 3t.\end{array} \right.\)

D. \(\left\{ \begin{array}{l}x = 2 - 5t\\y = 4t\\z =  - 3 + 3t.\end{array} \right.\)

A. \(\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1.\)

B. \(\frac{x}{3} + \frac{y}{2} + \frac{z}{4} = 1.\)

C. \(\frac{x}{3} + \frac{y}{2} + \frac{z}{4} = 0.\)

D. \(\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 0.\)

A. \(\overrightarrow {{n_1}}  = \left( {2;3; - 1} \right).\)

B. \(\overrightarrow {{n_2}}  = \left( {1;3;2} \right).\)

C. \(\overrightarrow {{n_3}}  = \left( {2; - 3;1} \right).\)

D. \(\overrightarrow {{n_4}}  = \left( { - 1;3;2} \right).\)

A. \(\frac{{\pi {a^2}\sqrt {17} }}{6}\)      B. \(\frac{{\pi {a^2}\sqrt {17} }}{4}\)

C. \(\frac{{\pi {a^2}\sqrt {17} }}{8}\)      D. \(\frac{{\pi {a^2}\sqrt {15} }}{4}\)

A. \(\frac{{x - 1}}{1} = \frac{{y + 2}}{2} = \frac{{z - 1}}{{ - 3}}\).

B. \(\frac{{x + 1}}{1} = \frac{{y - 2}}{{ - 2}} = \frac{{z - 1}}{3}\).

C. \(\frac{{x + 1}}{1} = \frac{{y - 2}}{{ - 2}} = \frac{{z + 5}}{3}\).

D. \(\frac{{x - 1}}{1} = \frac{{y + 2}}{{ - 2}} = \frac{{z + 1}}{3}\).

A. \(x - y + 3z - 6 = 0\).

B. \( - x + y - 3z = 0\)

C. \( - x + y + 3z = 0\)

D. \( - x - y + 3z = 0\)

A. \(\left\{ \begin{array}{l}x = 1 + t\\y = 1 + t\\z = 3 + 3t\end{array} \right.\). 

B. \(\left\{ \begin{array}{l}x = 1 + 2t\\y = 1 - t\\z = 3\end{array} \right.\).

C. \(\left\{ \begin{array}{l}x =  - 12 + t\\y = 6 + t\\z = 3t\end{array} \right.\).

D. \(\left\{ \begin{array}{l}x = 1 - 2t\\y = 1 + t\\z = 3 - t\end{array} \right.\)

A. \(\left( {0; - 2;1} \right)\).

B. \(\left( {0;0;1} \right)\).

C. \(\left( {3;0;1} \right)\).

D. \(\left( {3; - 2;0} \right)\).

A. \(\frac{{2a}}{3}\).                               

B. \(\frac{a}{2}\).

C. \(\frac{{a\sqrt 2 }}{2}\).                       

D. \(\frac{{2a\sqrt 5 }}{5}\).

A. \(2\).                    B. \(8\).

C. \(12\).                  D. \(3\).

A. \(\left( { - 2;3;4} \right)\).

B. \(\left( {2; - 3;4} \right)\).

C. \(\left( {2; - 3;0} \right)\).

D. \(\left( {2; - 3;1} \right)\).

A. \(\left( {5;1; - 4} \right)\).

B. \(\left( { - 1; - 1;1} \right)\).

C. \(\left( {3;5; - 3} \right)\).

D. \(\left( {1;2;2} \right)\).

A. \( - x + y + z - 6 = 0\).

B. \(x - y - z + 4 = 0\).

C. \(x - y - z + 1 = 0\).

D. \(x - y - z - 2 = 0\).

A. \(\frac{{3{a^3}}}{8}\).                        B. \(\frac{{5{a^3}}}{8}\).

C. \(\frac{{10{a^3}}}{{12}}\).                 D. \(\frac{{3{a^3}}}{4}\).

A. \(2{a^3}\).           

B. \({a^3}\sqrt 3 \).   

C. \(\frac{{{a^3}\sqrt 3 }}{3}\).       

D. \(6{a^3}\).

A. \(5\)                     B. \(4\)

C. \(2\sqrt 5 \)           D. \(\sqrt {52} \)