Trắc nghiệm Phương trình mặt phẳng Toán Lớp 12

A. (P):x – 3y – 2z – 1 = 0

B. (P):x – 3y – 2z + 1 = 0

C. (P):x + 3y – 2z – 13 = 0

D. (P):x + 3y – 2z + 13 = 0

A. x + y + z – 3 = 0

B. y – 2 = 0

C. x + 1 = 0

D. x - 1 = 0

A. \(\frac{1}{4} .\)

B. \(\frac{1}{2} .\)

C. \(\frac{1}{5} .\)

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

A. \(C\left(0 ;-\frac{2+\sqrt{2}}{0} ; 0\right) .\)

B. \(C\left(0 ; \frac{1}{4} ; 0\right) . \)

C. \( C\left(0 ; \frac{2+\sqrt{2}}{2} ; 0\right) .\)

D. \(C\left(0 ;-\frac{1}{4} ; 0\right) .\)

A. \(\begin{aligned} &2 \sqrt{2} \end{aligned}\)

B. \(\begin{aligned} &2 \sqrt{3} \end{aligned}\)

C. \(\begin{aligned} &3 \sqrt{2} \end{aligned}\)

D. \(\begin{aligned} &3 \sqrt{3} \end{aligned}\)

A. 2

B. 3

C. 4

D. 5

A. \(2 \sqrt{6}\)

B. \(4 \sqrt{6}\)

C. \(6\sqrt{6}\)

D. \(8 \sqrt{6}\)

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

B. \(\left(x-\frac{3}{2}\right)^{2}+\left(y+\frac{3}{2}\right)^{2}+\left(z-\frac{3}{2}\right)^{2}=\frac{27}{4}\)

C. \(\left(x-\frac{3}{2}\right)^{2}+\left(y-\frac{3}{2}\right)^{2}+\left(z+\frac{3}{2}\right)^{2}=\frac{27}{4}\)

D. \(\left(x-\frac{3}{2}\right)^{2}+\left(y-\frac{3}{2}\right)^{2}+\left(z-\frac{3}{2}\right)^{2}=\frac{27}{4}\)

A. \(\frac{9}{2} .\)

B. \(\frac{9}{4} .\)

C. \(1\)

D. 2

A. 0

B. -1

C. -3

D. 2

A. 2x – 5y + z – 17 = 0

B. 2x – 5y + z + 17 = 0

C. 2x – 5y + z – 12 = 0

D. 2x – 3y – 2z – 18 = 0

A. x – 2y + 3z + 6 = 0

B. x – 2y + 3z – 6 = 0

C. x + 2y – 3z – 6 = 0

D. x + 2y – 3z + 6 = 0

A. \(\overrightarrow {{n_1}} = \left( {1; – 1;4} \right)\)

B. \(\overrightarrow {{n_4}} = \left( {1; – 2;2} \right)\)

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

D. \(\overrightarrow {{n_3}} = \left( { – 2;2; – 1} \right)\)

A. \(\vec u = \left( {0;{\mkern 1mu} 1;{\mkern 1mu} – 2} \right)\)

B. \(\vec v = \left( {1;{\mkern 1mu} – 2;{\mkern 1mu} 3} \right)\)

C. \(\vec n = \left( {2;{\mkern 1mu} 0;{\mkern 1mu} – 1} \right)\)

D. \(\vec w = \left( {1;{\mkern 1mu} – 2;{\mkern 1mu} 0} \right)\)

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

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

C. \(\overrightarrow n = \left( { – 2;\;1;\; – 3} \right)\)

D. \(\overrightarrow n = \left( {2;\;1;\; – 3} \right)\)

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

B. \(\overrightarrow n = \left( { – 6; – 3;9} \right)\)

C. \(\overrightarrow n = \left( {6; – 3; – 9} \right)\)

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

A. \(\overrightarrow n = \left( { – 2;3;1} \right)\)

B. \(\overrightarrow n = \left( {2;3; – 4} \right)\)

C. \(\overrightarrow n = \left( {2; – 3;4} \right)\)

D. \(\overrightarrow n = \left( { – 2;3;4} \right)\)

A. \(\overrightarrow n = \left( {6;\,\,4;\,\,0} \right)\) là một vectơ pháp tuyến của mặt phẳng \(\left( P \right).\)

B. \(\overrightarrow n = \left( {6;\,\,4; – 6} \right)\) là một vectơ pháp tuyến của mặt phẳng \(\left( P \right).\)

C. \(\overrightarrow n = \left( {3;\,\,2; – 3} \right)\) là một vectơ pháp tuyến của mặt phẳng \(\left( P \right).\)

D. \(\overrightarrow n = \left( {3;\,\,2;\,\,3} \right)\) là một vectơ pháp tuyến của mặt phẳng \(\left( P \right).\)

A. x = y + z

B. y – z = 0

C. y + z = 0

D. x = 0

A. x = 0

B. y + z = 0

C. z = 0

D. x + y = 0

A. \(\overrightarrow n = \left( { – 3;{\rm{ }} – 9{\rm{; 15}}} \right)\)

B. \(\overrightarrow n = \left( { – 1; – 3{\rm{; 5}}} \right)\)

C. \(\overrightarrow n = \left( {2;{\rm{ 6; }} – {\rm{10}}} \right)\)

D. \(\overrightarrow n = \left( { – 2;{\rm{ }} – {\rm{6; }} – {\rm{10}}} \right)\)

A. y – 2 = 0

B. x – 2 = 0

C. y – z = 0

D. x – y = 0

A. \(B\left( {1; – 2;4} \right)\)

B. \(A\left( {1; – 2; – 4} \right)\)

C. \(C\left( {1;2; – 4} \right)\)

D. \(D\left( { – 1; – 2; – 4} \right)\)

A. \(\left( R \right):x + y – 7 = 0\)

B. \(\left( S \right):x + y + z + 5 = 0\)

C. \(\left( Q \right):x – 1 = 0\)

D. \(\left( P \right):z – 2 = 0\)

A. \(\left( P \right):x + y + z = 0\)

B. \(\left( \alpha \right):x + y + 2z = 0\)

C. \(\left( \beta \right):x + y – z = 0\)

D. \(\left( Q \right):x + y – 2z = 0\)

A. x + y = 0

B. x + 2y = 0

C. x – y = 0

D. x + y – 1 = 0

A. 2x + 3y + 4 = 0

B. x – 2y + 2x = 0

C. x – 2y + 2z + 8 = 0

D. x – 2y + 2z + 4 = 0

A. x = y + z

B. y – z = 0

C. y + z = 0

D. x = 0

A. \({\vec n_3} = \left( {2;\, – 3;\,4} \right)\)

B. \({\vec n_1} = \left( {2;\,0;\, – 3} \right)\)

C. \({\vec n_2} = \left( {3;\,0;\,2} \right)\)

D. \({\vec n_4} = \left( {2;\, – 3;\,0} \right)\)

A. \(\overrightarrow {{n_2}} = \left( {3;\,2;\,4} \right)\)

B. \(\overrightarrow {{n_3}} = \left( {2;\, – 4;\,1} \right)\)

C. \(\overrightarrow {{n_1}} = \left( {3;\, – 4;\,1} \right)\)

D. \(\overrightarrow {{n_4}} = \left( {3;\,2;\, – 4} \right)\)

A. \(\frac{5 \sqrt{11}}{11}\)

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

C. 7

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

A. \(M(2 ; 1 ;-1)\)

B. \(Q(1 ; 1 ; 1)\)

C. \(N(2 ; 1 ; 1)\)

D. \(P(1 ;-1 ; 1)\)

A. \(\frac{9}{\sqrt{14}}\)

B. \(\frac{3}{\sqrt{14}}\)

C. \(\sqrt{14}\)

D. \(3\sqrt{14}\)

A. \(\begin{aligned} &2 x+4 y+6 z+1=0 . \end{aligned}\)

B. \( x-2 y+3 z+1=0 \text { . }\)

C. \(x+2 y-3 z-1=0 \text { . }\)

D. \( 2 x-4 z+6=0\)

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

B. \(y-2 z+1=0\)

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

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

A. \(N(1 ; 0 ; 3) .\)

B. \(P(1 ; 0 ; 0) . \)

C. \(Q(0 ; 2 ; 0) . \)

D. \(M(0 ; 2 ; 3) \text { . }\)

A. \(\vec{n}=(-2 ;-3 ; 5).\)

B. \( \vec{n}=(-2 ; 3 ; 5).\)

C. \(\vec{n}=(2 ; 3 ; 5).\)

D. \(\vec{n}=(2 ;-3 ; 5).\)

A. \(\begin{array}{llll} x-2 z-1=0 \end{array}\)

B. \( y-2=0 . \)

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

D. \( x+z=0 .\)

A. \(\vec{n}=(-2 ;-3 ; 1) \)

B. \(\vec{n}=(-2 ;-3 ; 0) . \)

C. \(\vec{n}=(2 ; 3 ; 1) .\)

D. \(\vec{n}=(2 ; 3 ; 2)\)

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

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

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

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

A. \(\vec{n}=(3 ;-2 ; 6)\)

B. \(\vec{n}=(1;-2 ; 3)\)

C. \(\vec{n}=(-1 ;-1 ; 1)\)

D. \(\vec{n}=(-2 ;3 ; 5)\)

A. \(90^{\circ} .\)

B. \(30^{\circ} .\)

C. \(60^{\circ} .\)

D. \(45^{\circ} .\)

A. \(\frac{4}{3}\)

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

C. \(\frac{\sqrt2}{3}\)

D. 1

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

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

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

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

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

B. \(-2x+3y+4z=0\)

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

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

A. \(\vec{n}=(2 ; 3 ;-1)\)

B. \(\vec{n}=(2 ; 3 ; 0)\)

C. \(\vec{n}=(-2 ; 0 ;-3)\)

D. \(\vec{n}=(2 ; 0 ;-3)\)

A. 1

B. 2

C. 3

D. \(\frac{1}{2}\)

A. \(\vec{n}_{2}(2 ; 1 ;-1) \text { . }\)

B. \(\vec{n}_{1}(3 ; -1 ;-1) \text { . }\)

C. \(\vec{n}_{3}(1 ; 1 ;-1) \text { . }\)

D. \(\vec{n}_{4}(2 ; 0 ;-1) \text { . }\)

A. \(\begin{array}{ll} \left(\alpha_{1}\right): x-2 y+2 z-3=0 . \end{array}\)

B. \(\left(\alpha_{2}\right): 2 x+2 y-z+10=0 \)

C. \(\left(\alpha_{3}\right): x-2 y+2 z-1=0 .\)

D. \(\left(\alpha_{4}\right): 2 x-y+2 z+4=0\)

A. (0 ; 4 ; 0)

B. (0 ; 5 ; 0)

C. (0 ; 6 ; 0)

D. (0 ; 7 ; 0)