40 câu trắc nghiệm ôn tập Chương 3 Hình học 12

A. \(G\left( { - \frac{3}{2};\,3;\,0} \right).\)

B. \(G\left( { - 3;\,6;\,0} \right).\)

C. \(G\left( { - 1;\,2;\,0} \right).\)

D. \(G\left( { - \frac{1}{3};\,\frac{2}{3};\,0} \right).\)

A. \(AB = \sqrt {10} .\)

B. \(AB = 2\sqrt 2 .\)

C. \(AB = \sqrt {26} .\)

D. \(AB = \sqrt {34} .\)

A. (- 1;2;- 3)

B. (2;- 1;- 3)

C.
(- 3; 2; - 1)

D. (2; - 3; - 1)

A. (3;4;- 1)

B. (3;6;- 4)

C. (2;4; - 1)

D. (2;3;- 12)

A. \(\cos \left( {\overrightarrow {AB} ,\overrightarrow {AC} } \right) = \frac{{\overrightarrow {AB} .\overrightarrow {AC} }}{{AB.AC}}\)

B. \(\cos \left( {\widehat {AB,AC}} \right) = \frac{{\left| {\overrightarrow {AB} .\overrightarrow {CA} } \right|}}{{AB.AC}}\)

C. \({\overrightarrow {AB} ^2} = A{B^2}\)

D. \(\cos \left( {\widehat {AB,AC}} \right) = \frac{{\overrightarrow {AB} .\overrightarrow {AC} }}{{AB.AC}}\)

A. \(\frac{1}{6}\)

B. \(\frac{1}{3}\)

C. \(\frac{1}{3}\)

D. \(\frac{3}{2}\)

A. 30⁰

B. 60⁰

C. 90⁰

D. 120⁰

A. (0;1;0)

B. (1;0;0)

C. (0;1;1)

D. (1;1;0)

A. (8;- 12;5)

B. (8;- 12;0)

C. (0;8;12)

D. (0;8;- 12)

A. (10;9;2)

B. (9;10;2)

C. (10;9;9)

D. (9;2;10)

A. (0;6;-1)

B. (1;0;0)

C. (2;0;0)

D. (4;0;0)

A. (0;4;-1)

B. (2;0;0)

C. (0;4;1)

D. (0;4;4)

A. \(\left( { - 2;8; - \frac{5}{3}} \right)\)

B. \(\left( { - 2;8;5} \right)\)

C. (0;8;5)

D. (- 2;1;5)

A. 1

B. 2

C. 3

D. 4

A. \(A\left( {1;2;3} \right),\,B\left( { - 1;3;2} \right),\,C\left( {2;1;2} \right)\)

B. \(D\left( {2;3;1} \right),E\left( {1;1;1} \right),{\rm{ F}}\left( {3;2;3} \right)\)

C. \(G\left( {0;1;1} \right),\,I\left( {2;1;2} \right),\,H\left( {1;1;2} \right)\)

D. \(M\left( {1;1;1} \right),N\left( {2;3; - 1} \right),P\left( {3;5; - 3} \right)\)

A. B(1;2;3)

B. B(- 2;2;0)

C. B(2;- 2;0)

D. B(4;2;6)

A. m = 1

B. m = - 2

C. m = 5

D. m = - 8 

A. M'(0;0;5)

B. M'(1;- 2;0)

C. M'(1;0;5)

D. M'(0;- 2;5)

A. M'(0;0;3)

B. M'(0;- 1;0)

C. M'(4;0;0)

D. M'(2;0;0)

A. (0;1;6)

B. (5;0;0)

C. (0;3;1)

D. (- 4;0;0)

A. (0;1;0)

B. (0;3;0)

C. \(\left( {0;\frac{{ - 5}}{2};0} \right)\)

D. (2;0;3)

A. \(\sqrt {14} \)

B. \(\sqrt {15} \)

C. \(\sqrt {13} \)

D. 4

A. m = 4, n = 3

B. m = 4, n = - 3

C. m = - 4, n = 3

D. m = - 4, n = - 3

A. 4

B. 2

C. 3

D. 1

A. m = 1

B. m = 4

C. m = - 1

D. m = 1 hoặc m = 4

A. \(m = \frac{1}{4},n = \frac{7}{4},k = 3\)

B. \(m = \frac{5}{2},n = \frac{5}{2},k = \frac{3}{2}\)

C. \(m = \frac{5}{2},n = \frac{5}{2},k = \frac{5}{2}\)

D. \(m = \frac{7}{4},n = \frac{1}{4},k = 3\)

A. (- 1;2;1)

B. (1;- 2; - 1)

C. (1;- 2;1)

D. (1;2;2)

A. \({\left( {x - 1} \right)^2} + {\left( {y - 2} \right)^2} + {\left( {z - 3} \right)^2} = 14\)

B. \({x^2} + {y^2} + {z^2} = 14\)

C. \({\left( {x - 1} \right)^2} + {\left( {y - 2} \right)^2} + {\left( {z - 3} \right)^2} = \frac{7}{2}\)

D. \({x^2} + {y^2} + {z^2} = \frac{7}{2}\)

A. (0;0;-1)

B. (0;0;1)

C. (1;1;0)

D. (-1;-1;0)

A. \({x^2} + {y^2} + {z^2} - \frac{3}{2}x - z - \frac{5}{2} = 0\)

B. \({x^2} + {y^2} + {z^2} - \frac{3}{4}x + \frac{1}{2}z + \frac{5}{2} = 0\)

C. \({x^2} + {y^2} + {z^2} - \frac{3}{2}x + z - \frac{5}{2} = 0\)

D. \({x^2} + {y^2} + {z^2} - \frac{3}{2}y - z - \frac{5}{2} = 0\)

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

B. \(\frac{{3\sqrt 3 }}{4}\)

C. \(3\sqrt 3 \)

D. 3

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

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

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

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

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

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

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

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

A. \(2x + 2y + z + D = 0;D \ne  - 3\)

B. \(2x + y + 2z + D = 0;D \ne  - 3\)

C. \(x + 2y + 2z + D = 0;D \ne  - 3\)

D. \(2x + 2y - 3z + D = 0;D \ne  - 3\)

A. \(d:\left\{ \begin{array}{l}
x =  - 3 + 4t\\
y =  - 1 + 3t\\
z = 6 - 3t.
\end{array} \right.\)

B. \(d:\left\{ \begin{array}{l}
x =  - 1 + 4t\\
y =  - 2 + 3t\\
z =  - 3 - 3t.
\end{array} \right.\)

C. \(d:\left\{ \begin{array}{l}
x = 1 + 4t\\
y = 2 + 3t\\
z = 3 - t.
\end{array} \right.\)

D. \(d:\left\{ \begin{array}{l}
x = 1 - 4t\\
y = 2 - 3t\\
z = 3 - 3t.
\end{array} \right.\)

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

B. \(d:\frac{{x + 1}}{1} = \frac{{y + 1}}{1} = \frac{{z + 1}}{1}\)

C. \(d:\frac{{x - 1}}{1} = \frac{{y - 1}}{1} = \frac{{z - 1}}{1}\)

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

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

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

C. \(\Delta :\frac{{x - 1}}{{ - 1}} = \frac{{y - 2}}{2} = \frac{{z - 1}}{1}\)

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

A. \(d:\left\{ {\begin{array}{*{20}{c}}
{x = 1 + t}\\
{y = 1 - 2t}\\
{z = 1 + 4t}
\end{array}} \right.\)

B. \(d:\left\{ {\begin{array}{*{20}{c}}
{x = 1 + t}\\
{y = 1 + 2t}\\
{z = 1 + 4t}
\end{array}} \right.\)

C. \(d:\left\{ {\begin{array}{*{20}{c}}
{x = 1 + t}\\
{y =  - 2 + t}\\
{z =  - 4 + t}
\end{array}} \right.\)

D. \(d:\left\{ {\begin{array}{*{20}{c}}
{x =  - 1 + t}\\
{y =  - 1 - 2t}\\
{z =  - 1 + 4t}
\end{array}} \right.\)

A. \(2x + 3y + z + 6 = 0.\)

B. \(2x - 3y + z - 6 = 0.\)

C. \(2x - 3y + z + 6 = 0.\)

D. \(2x + 3y + z - 6 = 0.\)