Trắc nghiệm: Tích vô hướng của hai vectơ có đáp án

A. 10

B. -10

C. $10\sqrt{3}$

D. $-10\sqrt{3}$

A . 1

B. -1

C. 29

D. -29

A. 15

B. 21

C. -15

D. -21

A. $\stackrel{\to }{a},\stackrel{\to }{b}$ cùng hướng khi và chỉ khi $\stackrel{\to }{a}.\stackrel{\to }{b}=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

B. $\stackrel{\to }{a},\stackrel{\to }{b}$ cùng hướng khi và chỉ khi $\stackrel{\to }{a}.\stackrel{\to }{b}=-\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

C. $\stackrel{\to }{a},\stackrel{\to }{b}$ cùng hướng khi và chỉ khi $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

A. $A{B}^2$

B. $A{C}^2$

C. $A{D}^2$

D. 0

A. $\stackrel{\to }{MA}.\stackrel{\to }{MB}=M{I}^2+I{A}^2$

B. $\stackrel{\to }{MA}.\stackrel{\to }{MB}=M{I}^2-I{A}^2$

C. $\stackrel{\to }{MA}.\stackrel{\to }{MB}=2M{I}^2-I{A}^2$

D. $\stackrel{\to }{MA}.\stackrel{\to }{MB}=M{I}^2-2I{A}^2$

A. 5

B. -5

C. 7

D. -7

A. 17

B. 169

C. 13

D. $\sqrt{159}$

A. $0°$

B. $30°$

C. $45°$

D. $60°$

A.( 5/2; -9/2)

B. (- 5/2; 9/2)

C. (-2; 4)

D. (-3;5)

A. (2; 2)

B. (1; 1)

C.( -2; -2)

D. (-1; -1)

A. 5/8

B. 5/4

C. 5/16

D. 0, 5

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

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

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

D. $\stackrel{\to }{a}.\stackrel{\to }{b}=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right).\cos \left(\stackrel{\to }{a},\stackrel{\to }{b}\right)$

A. 40

B. $-40\sqrt{3}$

C. $40\sqrt{3}$

D. -40

A. 12

B. -12

C. $12\sqrt{3}$

D. $-12\sqrt{3}$

A. $a^2$

B. $\frac{1}{2}{a}^2$

C.- $\frac{1}{2}{a}^2$

D. $2a^2$

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

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

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

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

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

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

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

A. $\stackrel{\to }{a}\perp \stackrel{\to }{b}\iff \stackrel{\to }{a}.\stackrel{\to }{b}=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

B. $\stackrel{\to }{a}\perp \stackrel{\to }{b}\iff \stackrel{\to }{a}.\stackrel{\to }{b}=0$

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

D. $a⃗\perp b⃗⟺a{⃗}^2=b{⃗}^2$

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

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

C. $\stackrel{\to }{a}.\stackrel{\to }{b}<\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

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

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

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

C. $\stackrel{\to }{a}.\stackrel{\to }{b}<\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

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

A. $\exists \stackrel{\to }{a},{\left(\stackrel{\to }{a}\right)}^2=\left({\stackrel{\to }{a}}^2\right)$

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

C. $\forall \stackrel{\to }{a},{\left(\stackrel{\to }{a}\right)}^2<0$

D. $\forall \stackrel{\to }{a},{\left(\stackrel{\to }{a}\right)}^2>0$

A. $\stackrel{\to }{a},\stackrel{\to }{b}$ cùng phương khi và chỉ khi $\stackrel{\to }{a}.\stackrel{\to }{b}=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

B. $\stackrel{\to }{a},\stackrel{\to }{b}$ cùng phương khi và chỉ khi $\stackrel{\to }{a}.\stackrel{\to }{b}=-\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

C. $\stackrel{\to }{a},\stackrel{\to }{b}$ cùng phương khi và chỉ khi $\stackrel{\to }{a}.\stackrel{\to }{b}\ne \left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

D. $\stackrel{\to }{a},\stackrel{\to }{b}$ cùng phương khi và chỉ khi $\left(\stackrel{\to }{a}.\stackrel{\to }{b}\right)=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

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

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

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

A. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=90°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=\stackrel{\to }{0}$

B. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=90°\iff \stackrel{\to }{a}.\stackrel{\to }{b}\ne 0$

C. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=90°\iff \stackrel{\to }{a}.\stackrel{\to }{b}\ne \stackrel{\to }{0}$

D. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=90°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=0$

A. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=0°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=0$

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

C. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=0°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=-\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

D. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=0°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=\stackrel{\to }{0}$

A. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=180°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=0$

B. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=180°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

C. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=180°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=-\left(\stackrel{\to }{a}\right).\left(\stackrel{\to }{b}\right)$

D. $\left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=180°\iff \stackrel{\to }{a}.\stackrel{\to }{b}=\stackrel{\to }{0}$

A. $\stackrel{\to }{a}.\stackrel{\to }{b}=0\iff \left(\begin{array}{c}\stackrel{\to }{a}=\stackrel{\to }{0}\\ \stackrel{\to }{b}=\stackrel{\to }{0}\end{array}\right)$

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

C. $\stackrel{\to }{a}.\stackrel{\to }{b}=0\iff \left(\begin{array}{c}\stackrel{\to }{a}=\stackrel{\to }{0}\\ \stackrel{\to }{b}=\stackrel{\to }{0}\end{array}\right)$

D. $\stackrel{\to }{a}.\stackrel{\to }{b}\iff \left(\begin{array}{c}\stackrel{\to }{a}=\stackrel{\to }{0}\\ \stackrel{\to }{b}=\stackrel{\to }{0}\\ \stackrel{\to }{a}\perp \stackrel{\to }{b}\end{array}\right)$

A. $\stackrel{\to }{AM}.\stackrel{\to }{AB}=-AM.AB$

B. $\stackrel{\to }{AM}.\stackrel{\to }{AB}=AM.AB$

C. $\stackrel{\to }{AM}.\stackrel{\to }{AB}<0$

D. $\stackrel{\to }{AM}.\stackrel{\to }{AB}>AM.AB$

A. $\stackrel{\to }{MA}.\stackrel{\to }{MB}>0$

B. $\stackrel{\to }{MA}.\stackrel{\to }{MB}<-MA.MB$

C. $\stackrel{\to }{MA}.\stackrel{\to }{MB}=-MA.MB$

D. $\stackrel{\to }{MA}.\stackrel{\to }{MB}=MA.MB$

A. $\stackrel{\to }{0}$

B.0

C. $A{B}^2$

D. $\frac{1}{2}A{B}^2$

A. $\stackrel{\to }{0}$

B.0

C. $A{B}^2$

D. $B{C}^2$

A. $\stackrel{\to }{0}$

B.0

C. $A{B}^2+B{C}^2+C{A}^2$

D. $\frac{1}{2}\left(A{B}^2+B{C}^2+C{A}^2\right)$

A. $a^2$

B. $-\frac{1}{2}{a}^2$

C. $-a^2$

D. $-\frac{\sqrt{3}}{2}{a}^2$

A. $-a^2$

B. $a^2$

C. $-\frac{1}{2}{a}^2$

D. $2a^2$

A. $a^2$

B. $\frac{1}{2}{a}^2$

C. $-\frac{1}{2}{a}^2$

D. $\frac{\sqrt{3}}{2}{a}^2$

A. $a^2$

B. $\frac{1}{2}{a}^2$

C.- $\frac{1}{2}{a}^2$

D. $-\frac{\sqrt{3}}{2}{a}^2$

A. $\stackrel{\to }{BA}.\stackrel{\to }{BC}=b^2.$

B. $\stackrel{\to }{BA}.\stackrel{\to }{BC}=c^2.$

C. $\stackrel{\to }{BA}.\stackrel{\to }{BC}=b^2+c^2.$

D. $\stackrel{\to }{BA}.\stackrel{\to }{BC}=b^2-c^2.$

A.-1

B. $3a^2$

C. $-3a^2$

D. $2a^2$

A.0

B.3

C.81

D.9

A.1

B.-1

C.-56

D.56

A. x = - 2

B. x = 2

C. x = -3

D. x = 3

A. $x=\sqrt{19}$

B. $x=-\sqrt{19}$

C. $x=\sqrt{21}$

D. $x\in \left(-\sqrt{19};\sqrt{19}\right)$

A. $\stackrel{\to }{0}$

B. $C{D}^2$

C.0

D. $A{B}^2+A{C}^2+A{D}^2$

A.1

B.0

C. $A{B}^2-B{C}^2$

D. $A{B}^2+B{C}^2$

A.1

B. $-A{B}^2$

C.0

D. $A{B}^2$

A. $\stackrel{\to }{a}.\stackrel{\to }{0}=\stackrel{\to }{0}$

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

C. $\stackrel{\to }{a}.\stackrel{\to }{0}=0$

D. $\stackrel{\to }{a}.\stackrel{\to }{0}=-\left(\stackrel{\to }{a}\right)$

A. 40

B. – 40

C. 26

D. – 26

A. – 30

B. 3

C. 30

D. 43

A. $\stackrel{\to }{c}=\left(-1;-3\right).$

B. $\stackrel{\to }{c}=\left(-1;3\right).$

C. $\stackrel{\to }{c}=\left(1;-3\right).$

D. $\stackrel{\to }{c}=\left(1;3\right).$

A. $\cos \left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=\frac{1}{\sqrt{2}}.$

B. $\cos \left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=-\frac{\sqrt{2}}{2}.$

C. $\cos \left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=-\frac{1}{2\sqrt{2}}.$

D. $\cos \left(\stackrel{\to }{a},\stackrel{\to }{b}\right)=\frac{1}{2}.$

A.90 ⁰

B. 60 ⁰

C. 45 ⁰

D. 30 ⁰

A. 15 ⁰

B.60 ⁰

C. 120 ⁰

D. 135 ⁰ .

A. k = 20

B. k = -20

C. k = -40

D. k= 40

A. $\stackrel{\to }{d}=\left(\frac{5}{7};\frac{6}{7}\right).$

B. $\stackrel{\to }{d}=\left(-\frac{5}{7};\frac{6}{7}\right).$

C. $\stackrel{\to }{d}=\left(\frac{5}{7};-\frac{6}{7}\right).$

D. $\stackrel{\to }{d}=\left(-\frac{5}{7};-\frac{6}{7}\right).$

A. m = 4

B. m = -4

C. m = -2

D. m = 2

A. m = 4

B. m = -1/2

C. m = -1/4

D. m = 1/2

A. $P=4+2\sqrt{2}.$

B. $P=4+4\sqrt{2}.$

C. $P=8+8\sqrt{2}.$

D. $P=2+2\sqrt{2}.$

A. $\stackrel{\to }{AC}\perp \stackrel{\to }{CB}.$

B. Tam giác ABC đều.

C. Tứ giác ABCD là hình vuông.

D. Tứ giác ABCD không nội tiếp đường tròn.

A. Tam giác ABC đều.

B. Tam giác ABC có ba góc đều nhọn.

C. Tam giác ABC cân tại B.

D. Tam giác ABC vuông cân tại A.

A. C (6; 0)

B. C (0; 0); C( 6; 0).

C. C(0; 0)

D.C(-1; 0)

A. M (-2; 0)

B. M(2; 0)

C. M(- 4; 0)

D. M(- 5; 0)

A. P(0; 4)

B. P(0; -4)

C. P(-4; 0)

D.P( 4; 0)

A. M(1; 0)

B.M(1; 0); M(- 3; 0)

C.M( 3; 0)

D. M(1; 0); M(3; 0)

A. $C\left(-\frac{5}{3};0\right).$

B. $C\left(\frac{5}{3};0\right).$

C. $C\left(-\frac{3}{5};0\right).$

D. $C\left(\frac{3}{5};0\right).$

A. M(0; 1)

B. M( 6; 0)

C. M(2; 0)

D. M(0; 6)

A. M(0; 1)

B. M (0; -1)

C. $M\left(0;\frac{1}{2}\right).$

D. $M\left(0;-\frac{1}{2}\right).$

A. D(2; -3)

B. D(2; 3)

C. D(-2; -3)

D. D(-2; 3)

A. $G\left(2;\frac{10}{3}\right).$

B. $G\left(\frac{8}{3};-\frac{10}{3}\right).$

C. $G\left(2;5\right).$

D. $G\left(\frac{4}{3};\frac{10}{3}\right).$

A. $I\left(\frac{1}{4};1\right).$

B. $I\left(-\frac{1}{4};1\right).$

C. $I\left(1;\frac{1}{4}\right).$

D. $I\left(1;-\frac{1}{4}\right).$

A. 5

B. 6

C. 7

D. 8

A. A’ (1; -4)

B. A’ (-1; 4)

C. A’ (1; 4)

D.A’ (4; 1)

A. C(4; 0)

B. C(- 2; 2)

C. C(4; 0); C( -2; 2)

D. C(2; 0)

A.D(0; -1)

B. D( 2; -3)

C. D( 2; -3); D(0; 1)

D. D( -2; -3)

A. $E=\left(\frac{5}{2};\frac{5}{2}\right).$

B. $E=\left(\frac{3}{2};-\frac{1}{2}\right).$

C. $E=\left(-2+3\sqrt{2};4+\sqrt{2}\right).$

D. $E=\left(-2+3\sqrt{2};4-\sqrt{2}\right).$