Cho hai vectơ a→, b→ tạo với nhau một góc 120o. Biết độ dài của hai vectơ đó lần lượt là 4 và 3. Độ dài của vectơ tổng a→+ b→ là

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: ${(\mathrm{x} - 1)}^2 + {(\mathrm{y} - 1)}^2 + {(\mathrm{z} - 2)}^2$ = 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. $\left|\overrightarrow{\mathrm{u}}\right|=\sqrt{{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2}$

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

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

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

A. ${\overrightarrow{\mathrm{u}}}^2={\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2$

B. ${\overrightarrow{\mathrm{u}}}^2=\overrightarrow{\mathrm{u}}.\overrightarrow{\mathrm{v}}\iff \overrightarrow{\mathrm{u}}=\overrightarrow{\mathrm{v}}$

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

D. $\cos \left(\overrightarrow{\mathrm{u}};\overrightarrow{\mathrm{v}}\right)=\frac{\overrightarrow{\mathrm{u}}.\overrightarrow{\mathrm{v}}}{\overrightarrow{\left|\mathrm{u}\right|}.\overrightarrow{\left|\mathrm{v}\right|}}$

A. $\left|\overrightarrow{\mathrm{u}}.\overrightarrow{\mathrm{v}}\right|=\overrightarrow{\left|\mathrm{u}\right|}.\overrightarrow{\left|\mathrm{v}\right|}$

B. $\overrightarrow{\mathrm{u}}.\overrightarrow{\mathrm{v}}>\overrightarrow{\left|\mathrm{u}\right|}.\overrightarrow{\left|\mathrm{v}\right|}$

C. $\left|\overrightarrow{\mathrm{u}}.\overrightarrow{\mathrm{v}}\right|=\overrightarrow{\left|\mathrm{u}\right|}.\overrightarrow{\left|\mathrm{v}\right|}.\left|\cos \left(\overrightarrow{\mathrm{u}},\overrightarrow{\mathrm{v}}\right)\right|$

D. $\overrightarrow{\mathrm{u}}.\overrightarrow{\mathrm{v}}<-\overrightarrow{\left|\mathrm{u}\right|}.\overrightarrow{\left|\mathrm{v}\right|}$

A. $\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}={\mathrm{x}}_1{\mathrm{x}}_2+{\mathrm{y}}_1{\mathrm{y}}_2+{\mathrm{z}}_1{\mathrm{z}}_2$

B. $\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}>\left|\overrightarrow{\mathrm{a}}\right|.\left|\overrightarrow{\mathrm{b}}\right|$

C. $\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}=\left|\overrightarrow{\mathrm{a}}\right|.\left|\overrightarrow{\mathrm{b}}\right|.\sin \left(\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}}\right)$

D. $\overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{b}}\iff {\mathrm{x}}_1^2+{\mathrm{y}}_1^2+{\mathrm{z}}_1^2={\mathrm{x}}_2^2+{\mathrm{y}}_2^2+{\mathrm{z}}_2^2$

A. (0;-1;-1)

B. (0;-3;-3)

C. (0;-2;-2)

D. Đáp án khác

A. $\left({\mathrm{x}}_{\mathrm{A}}+{\mathrm{x}}_{\mathrm{B}};{\mathrm{y}}_{\mathrm{A}}+{\mathrm{y}}_{\mathrm{B}};{\mathrm{z}}_{\mathrm{A}}+{\mathrm{z}}_{\mathrm{B}}\right)$

B. $\left({\mathrm{x}}_{\mathrm{B}}-{\mathrm{x}}_{\mathrm{A}};{\mathrm{y}}_{\mathrm{B}}-{\mathrm{y}}_{\mathrm{A}};{\mathrm{z}}_{\mathrm{B}}-{\mathrm{z}}_{\mathrm{A}}\right)$

C. $\left(\frac{{\mathrm{x}}_{\mathrm{A}}+{\mathrm{x}}_{\mathrm{B}}}{2};\frac{{\mathrm{y}}_{\mathrm{A}}+{\mathrm{y}}_{\mathrm{B}}}{2};\frac{{\mathrm{z}}_{\mathrm{A}}+{\mathrm{z}}_{\mathrm{B}}}{2}\right)$

D. $\left(\frac{{\mathrm{x}}_{\mathrm{B}}-{\mathrm{x}}_{\mathrm{A}}}{2};\frac{{\mathrm{y}}_{\mathrm{B}}-{\mathrm{y}}_{\mathrm{A}}}{2};\frac{{\mathrm{z}}_{\mathrm{B}}-{\mathrm{z}}_{\mathrm{A}}}{2}\right)$

A. $\mathrm{M}\left(\frac{{\mathrm{x}}_{\mathrm{B}}+{\mathrm{x}}_{\mathrm{C}}}{2};\frac{{\mathrm{y}}_{\mathrm{B}}+{\mathrm{y}}_{\mathrm{C}}}{2};\frac{{\mathrm{z}}_{\mathrm{B}}+{\mathrm{z}}_{\mathrm{C}}}{2}\right)$

B. $\overrightarrow{\mathrm{AB}}=\left({\mathrm{x}}_{\mathrm{B}}-{\mathrm{x}}_{\mathrm{A}};{\mathrm{y}}_{\mathrm{B}}-{\mathrm{y}}_{\mathrm{A}};{\mathrm{z}}_{\mathrm{B}}-{\mathrm{z}}_{\mathrm{A}}\right)$

C. $\mathrm{G}\left(\frac{{\mathrm{x}}_{\mathrm{A}}+{\mathrm{x}}_{\mathrm{B}}+{\mathrm{x}}_{\mathrm{C}}}{3};\frac{{\mathrm{y}}_{\mathrm{A}}+{\mathrm{y}}_{\mathrm{B}}+{\mathrm{y}}_{\mathrm{C}}}{3};\frac{{\mathrm{z}}_{\mathrm{A}}+{\mathrm{z}}_{\mathrm{B}}+{\mathrm{z}}_{\mathrm{C}}}{3}\right)$

D. $\mathrm{AB}=({\mathrm{x}}_{\mathrm{B}}-{\mathrm{x}}_{\mathrm{A}}{)}^2;{\left({\mathrm{y}}_{\mathrm{B}}-{\mathrm{y}}_{\mathrm{A}}\right)}^2; {\left(z_B-z_A\right)}^2$

A. $\overrightarrow{\mathrm{a}.}\left|\overrightarrow{\mathrm{b}}\right|=\left|\overrightarrow{\mathrm{a}}\right|.\overrightarrow{\mathrm{b}} \mathrm{với} \mathrm{mọi} \overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}}$

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

C. $\left|\overrightarrow{\mathrm{a}.}\overrightarrow{\mathrm{b}}\right|<\overrightarrow{\left|\mathrm{a}\right|}.\overrightarrow{\left|\mathrm{b}\right|} \mathrm{với} \mathrm{mọi} \overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}}$

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

A. $\left(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}\right).\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{b}}.\overrightarrow{\mathrm{c}}$

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

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

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

A. $\left(\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}\right)\overrightarrow{\mathrm{c}}={\mathrm{x}}_1{\mathrm{x}}_2{\mathrm{x}}_3+{\mathrm{y}}_1{\mathrm{y}}_2{\mathrm{y}}_3+{\mathrm{z}}_1{\mathrm{z}}_2{\mathrm{z}}_3$

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

C. $\left(\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}\right)\overrightarrow{\mathrm{c}}\ge \overrightarrow{0}$

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

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. ${\mathrm{M}}_1$(-1; 1; -1)

B. ${\mathrm{M}}_2$(1; -1; -1)

C. ${\mathrm{M}}_3$(-1; -1; 1)

D. ${\mathrm{M}}_4$(-1; -1; -1)

A. ${\mathrm{M}}_1$(2; 4; -6)

B. ${\mathrm{M}}_2$(-1; -2; 3)

C. ${\mathrm{M}}_3$(0; 0; 1)

D. ${\mathrm{M}}_4$(5; 10; -15)

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

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

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

D. $\overrightarrow{\mathrm{CB}}=3\overrightarrow{\mathrm{AB}}$

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

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

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

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

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