Bài tập 18 trang 130 SGK Hình học 12 NC

A. \({\left( {x - 3} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z + 5} \right)^2} = \frac{{361}}{{49}}\)

B. \({\left( {x - 3} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z + 5} \right)^2} = 49\)

C. \({\left( {x + 3} \right)^2} + {\left( {y + 4} \right)^2} + {\left( {z - 5} \right)^2} = 49\)

D. \({\left( {x + 3} \right)^2} + {\left( {y + 4} \right)^2} + {\left( {z - 5} \right)^2} = \frac{{361}}{{49}}\)

A. \({\left( {x - 1} \right)^2} + {\left( {y - 2} \right)^2} + {\left( {z - 1} \right)^2} = 81\)

B. \({\left( {x - 1} \right)^2} + {\left( {y - 2} \right)^2} + {\left( {z - 1} \right)^2} = 25\)

C. \({\left( {x - 1} \right)^2} + {\left( {y - 2} \right)^2} + {\left( {z - 1} \right)^2} = 5\)

D. \({\left( {x + 1} \right)^2} + {\left( {y + 2} \right)^2} + {\left( {z + 1} \right)^2} = 9\)

A. \(d = 9.\)                    B. \(d = \frac{{30}}{{13}}.\)

C. \(d = 6.\)                    D. \(d = \frac{{66}}{{13}}.\)

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

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

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

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

A. \(\overrightarrow {OM}  =  - 3\overrightarrow i  - 4\overrightarrow j  + 12\overrightarrow k \) 

B. \(\overrightarrow {OM}  =  - 3\overrightarrow i  + 4\overrightarrow j  - 12\overrightarrow k \)

C. \(\overrightarrow {OM}  = 3\overrightarrow i  + 4\overrightarrow j  + 12\overrightarrow k \)

D. \(\overrightarrow {OM}  = 3\overrightarrow i  - 4\overrightarrow j  + 12\overrightarrow k \)

A. \(\overrightarrow n  = \left( { - 5;1; - 2} \right)\)

B. \(\overrightarrow n  = \left( { - \frac{1}{5}; - 1; - \frac{1}{2}} \right)\)

C. \(\overrightarrow n  = \left( {2; - 10;5} \right)\)

D. \(\overrightarrow n  = \left( { - 2; - 10;20} \right)\)

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

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

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

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

A. \(A'\left( {2;0;5} \right)\)

B. \(A'\left( {0;3;5} \right)\)

C. \(A'\left( {0;3;0} \right)\)

D. \(A'\left( {2;0;0} \right)\)

A. \( - 2x + 5y + 2z - 28 = 0\)

B. \(x - 4y - 3z + 28 = 0\)

C. \(x - 4y - 3z - 28 = 0\)

D. \( - 2x + 5y + 2z + 28 = 0\)

A. \(V = \int\limits_0^\pi  {{{\cos }^2}xdx} \)

B. \(V = \pi \int\limits_0^\pi  {\left| {\cos x} \right|dx} \)

C. \(V = \pi \left| {\int\limits_0^\pi  {\left( { - \cos x} \right)dx} } \right|\)

D. \(V = \pi \int\limits_0^\pi  {{{\cos }^2}xdx} \)

A. \(x + y + z = 0.\)

B. \(x + y - z = 0.\)

C. \(x - y + z = 1.\)

D. \(x + y - z = 1.\)

A. \(\frac{{6\sqrt {41} }}{{41}}\)

B. \(\frac{{4\sqrt {41} }}{{41}}\)

C. \(\frac{{24\sqrt {41} }}{{41}}\)

D. \(\frac{{12\sqrt {41} }}{{41}}\)