60 câu trắc nghiệm: Hệ tọa độ trong không gian có đáp án (P1)

A. $\stackrel{\rightharpoonup }{b}=\left(4;2;-4\right)$

B. $\stackrel{\rightharpoonup }{b}=\left(-4;-2;4\right)$

C. $\stackrel{\rightharpoonup }{b}=\left(4;2;-4\right)\mathrm{hoặc}\stackrel{\rightharpoonup }{b}=\left(-4;-2;4\right)$

D. $\stackrel{\rightharpoonup }{b}=\left(12;6;-12\right)\mathrm{hoặc}\stackrel{\rightharpoonup }{b}=\left(-12;-6;12\right)$

A. m=1

B. m=1 hoặc m= -8

C. m= -8

D. Không tồn tại m thỏa mãn.

A. $\mathrm{cos\phi }=\frac{5}{\sqrt{364}}$

B. $\mathrm{cos\phi }=\frac{5}{\sqrt{312}}$

C. $\mathrm{cos\phi }=\frac{5}{364}$

D. $\mathrm{cos\phi }=\frac{5}{312}$

A. (4;-1;-1)

B. (2;3;-7)

C. (3/2; 1/2; -2)

D. (-2;-3;7)

A. (3;1;0)

B. (8;3;2)

C. (2;1;0)

D. (6;3;2)

A. 11

B. -1

C. 1

D. 0

A. Mặt cầu (S) có tâm I(1;1;2) và đường kính có độ dài bằng 2.

B. Phương trình chính tắc của mặt cầu (S) là: ${(x-1)}^2+{(y-1)}^2+{(z-2)}^2$ = 1

C. Diện tích của mặt cầu (S) là π

D. Thể tích của khối cầu (S) là 4π/3

A. I(2; -1; 0); R = 2 $\sqrt{3}$

B. I(4; -3; -2); R = 4 $\sqrt{3}$

C. I(3; -2; -1); R = 3 $\sqrt{3}$

D. I(3; -2; -1); R = 9

A. $\left(\stackrel{\to }{u}\right)=\sqrt{x^2+y^2+z^2}$

B. $\stackrel{\to }{u}+\stackrel{\to }{v}=\left(x+x\text{'};y+y\text{'};z+z\text{'}\right)$

C. $\stackrel{\to }{u}.\stackrel{\to }{v}=\left(x+y+z\right).\left(x\text{'}+y\text{'}+z\text{'}\right)$

D. $\stackrel{\to }{u}\perp \stackrel{\to }{v}\iff x.x\text{'}+y.y\text{'}+z.z\text{'}=0$

A. ${\stackrel{\to }{u}}^2=x^2+y^2+z^2$

B. ${\stackrel{\to }{u}}^2=\stackrel{\to }{u}.\stackrel{\to }{v}\iff \stackrel{\to }{u}=\stackrel{\to }{v}$

C. $\stackrel{\to }{u}-\stackrel{\to }{v}=\left(x-x\text{'};y-y\text{'};z-z\text{'}\right)$

D. $\cos \left(\stackrel{\to }{u};\stackrel{\to }{v}\right)=\frac{\stackrel{\to }{u}.\stackrel{\to }{v}}{\stackrel{\to }{\left(u\right)}.\stackrel{\to }{\left(v\right)}}$

A. $\left(\stackrel{\to }{u}.\stackrel{\to }{v}\right)=\stackrel{\to }{\left(u\right)}.\stackrel{\to }{\left(v\right)}$

B. $\stackrel{\to }{u}.\stackrel{\to }{v}>\stackrel{\to }{\left(u\right)}.\stackrel{\to }{\left(v\right)}$

C. $\left(\stackrel{\to }{u}.\stackrel{\to }{v}\right)=\stackrel{\to }{\left(u\right)}.\stackrel{\to }{\left(v\right)}.\left(\cos \left(\stackrel{\to }{u},\stackrel{\to }{v}\right)\right)$

D. $\stackrel{\to }{u}.\stackrel{\to }{v}<-\stackrel{\to }{\left(u\right)}.\stackrel{\to }{\left(v\right)}$

A. $\stackrel{\to }{a}.\stackrel{\to }{b}=x_1{x}_2+y_1{y}_2+z_1{z}_2$

B. $\stackrel{\to }{a}.\stackrel{\to }{b}>\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

C. $\stackrel{\to }{a}.\stackrel{\to }{b}=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right).\sin \left(\stackrel{\to }{a},\stackrel{\to }{b}\right)$

D. $\stackrel{\to }{a}=\stackrel{\to }{b}\iff x_1^2+y_1^2+z_1^2=x_2^2+y_2^2+z_2^2$

A. (0;-1;-1)

B. (0;-3;-3)

C. (0;-2;-2)

D. Đáp án khác

A. $\left(x_A+x_B;y_A+y_B;z_A+z_B\right)$

B. $\left(x_B-x_A;y_B-y_A;z_B-z_A\right)$

C. $\left(\frac{x_A+x_B}{2};\frac{y_A+y_B}{2};\frac{z_A+z_B}{2}\right)$

D. $\left(\frac{x_B-x_A}{2};\frac{y_B-y_A}{2};\frac{z_B-z_A}{2}\right)$

A. $M\left(\frac{x_B+x_C}{2};\frac{y_B+y_C}{2};\frac{z_B+z_C}{2}\right)$

B. $\stackrel{\to }{\mathrm{AB}}=\left(x_B-x_A;y_B-y_A;z_B-z_A\right)$

C. $G\left(\frac{x_A+x_B+x_C}{3};\frac{y_A+y_B+y_C}{3};\frac{z_A+z_B+z_C}{3}\right)$

D. $\mathrm{AB}=(x_B-x_A{)}^2;{\left(y_B-y_A\right)}^2;{\left(z_B-z_A\right)}^2$

A. $\stackrel{\to }{a.}\left(\stackrel{\to }{b}\right)=\left(\stackrel{\to }{a}\right).\stackrel{\to }{b}\mathrm{với}\mathrm{mọi}\stackrel{\to }{a},\stackrel{\to }{b}$

B. ${\left(\stackrel{\to }{a.}\stackrel{\to }{b}\right)}^2={\stackrel{\to }{a}}^2.{\stackrel{\to }{b}}^2\mathrm{với}\mathrm{mọi}\stackrel{\to }{a},\stackrel{\to }{b}$

C. $\left(\stackrel{\to }{a.}\stackrel{\to }{b}\right)<\stackrel{\to }{\left(a\right)}.\stackrel{\to }{\left(b\right)}\mathrm{với}\mathrm{mọi}\stackrel{\to }{a},\stackrel{\to }{b}$

D. $\stackrel{\to }{a.}\stackrel{\to }{b}=0\iff \stackrel{\to }{a}=\stackrel{\to }{0}\mathrm{hoặc}\stackrel{\to }{b}=\stackrel{\to }{0}$

A. $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right).\stackrel{\to }{c}=\left(\stackrel{\to }{b}.\stackrel{\to }{c}\right).\stackrel{\to }{a}\mathrm{với}\mathrm{mọi}\stackrel{\to }{a},\stackrel{\to }{b},\stackrel{\to }{c}$

B. $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right).\stackrel{\to }{c}=\left(\stackrel{\to }{b}.\stackrel{\to }{c}\right).\stackrel{\to }{a}\iff \stackrel{\to }{b}=\stackrel{\to }{0}$

C. $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right).\stackrel{\to }{c}=\left(\stackrel{\to }{b}.\stackrel{\to }{c}\right).\stackrel{\to }{a}\iff \stackrel{\to }{a}//\stackrel{\to }{c}$

D. $\left(\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right).\stackrel{\to }{c}\right)\le \left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right).\left(\stackrel{\to }{c}\right)$

A. $\left(\stackrel{\to }{a}+\stackrel{\to }{b}\right).\stackrel{\to }{c}=\stackrel{\to }{a}.\stackrel{\to }{c}+\stackrel{\to }{b}.\stackrel{\to }{c}$

B. ${\left(\stackrel{\to }{a}+\stackrel{\to }{b}\right)}^2={\stackrel{\to }{a}}^2+2\stackrel{\to }{a}\stackrel{\to }{b}+{\stackrel{\to }{b}}^2$

C. $\mathrm{Nếu}\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)\stackrel{\to }{c}=\stackrel{\to }{0}\mathrm{và}\stackrel{\to }{c}\ne 0\mathrm{thì}\stackrel{\to }{a}\perp \stackrel{\to }{b}$

D. $\mathrm{Nếu}\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)\stackrel{\to }{c}=\left(\stackrel{\to }{c}.\stackrel{\to }{b}\right)\stackrel{\to }{a}\mathrm{thì}\stackrel{\to }{a}\perp \stackrel{\to }{c}$

A. $\left(\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)\stackrel{\to }{c}\right)=\left(\left(\stackrel{\to }{c}.\stackrel{\to }{b}\right)\stackrel{\to }{a}\right)\mathrm{với}\mathrm{mọi}\stackrel{\to }{a},\stackrel{\to }{b},\stackrel{\to }{c}$

B. $\left(\stackrel{\to }{b}+\stackrel{\to }{a}\right)\stackrel{\to }{c}=\stackrel{\to }{a}.\stackrel{\to }{c}+\stackrel{\to }{b}.\stackrel{\to }{c}$

C. $\left(\stackrel{\to }{b}.\stackrel{\to }{c}\right)\stackrel{\to }{a}\ge 0$

D. ${\left(\stackrel{\to }{a}+\stackrel{\to }{b}+\stackrel{\to }{c}\right)}^2<0$

A. $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)\stackrel{\to }{c}=x_1{x}_2{x}_3+y_1{y}_2{y}_3+z_1{z}_2{z}_3$

B. $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)\stackrel{\to }{c}=\stackrel{\to }{0}\mathrm{khi}\mathrm{và}\mathrm{chỉ}\mathrm{khi}\stackrel{\to }{a}\perp \stackrel{\to }{b}\mathrm{hoặc}\stackrel{\to }{c}=\stackrel{\to }{0}$

C. $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)\stackrel{\to }{c}\ge \stackrel{\to }{0}$

D. $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)\stackrel{\to }{c}=\left(\stackrel{\to }{c}.\stackrel{\to }{b}\right)\stackrel{\to }{a}\mathrm{với}\mathrm{mọi}\stackrel{\to }{a},\stackrel{\to }{b},\stackrel{\to }{c}$

A. (3;-15;-4)

B. (-1;-9;-2)

C. (-3;15;4)

D. (1;9;2)

A. (4;3;9)

B. (4;3;21)

C. (2;-1;10)

D. (4;-1;10)

A. $\sqrt{16}$

B. $\sqrt{26}$

C. $2\sqrt{2}$

D. $\sqrt{66}$

A. 7

B. 1

C. $\sqrt{13}$

D. $\sqrt{37}$

A. 15

B. 5

C. 75

D. $\sqrt{75}$

A. $M_1$ (-1; 1; -1)

B. $M_2$ (1; -1; -1)

C. $M_3$ (-1; -1; 1)

D. $M_4$ (-1; -1; -1)

A. $M_1$ (2; 4; -6)

B. $M_2$ (-1; -2; 3)

C. $M_3$ (0; 0; 1)

D. $M_4$ (5; 10; -15)

A. A, B, C là ba đỉnh của một tam giác

B. $\stackrel{\to }{\mathrm{BC}}=-3\stackrel{\to }{\mathrm{BA}}$

C. $\stackrel{\to }{\mathrm{AC}}=-4\stackrel{\to }{\mathrm{AB}}$

D. $\stackrel{\to }{\mathrm{CB}}=3\stackrel{\to }{\mathrm{AB}}$

A. m = -1/3

B. m = -1/2

C. m = 1

D. m = 0

A. m = 1/2

B. m = 1 hoặc m = 1/2

C. m = 1

D. Không tồn tại m thỏa mãn