Д а н о в е к т о р А С → ( 5 ; − 1 ; 10 ) . Дано\ вектор\ \overrightarrow{АС}\left(5;-1;10\right). Д а н о в е к т о р А С <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> ( 5 ; − 1 ; 1 0 ) . Знайдіть його модуль.

126 \sqrt{126} 1 2 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

124 \sqrt{124} 1 2 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

16 \sqrt{16} 1 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

14 \sqrt{14} 1 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Знайдіть модуль вектора 1 2 с → , \frac{1}{2}\ \overrightarrow{с\ }, 2 1 с <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> , якщо с → ( − 4 ; 2 ; 6 ) \overrightarrow{с\ }\left(-4;2;6\right) с <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> ( − 4 ; 2 ; 6 )

14 \sqrt{14} 1 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

6 \sqrt{6} 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

56 \sqrt{56} 5 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Скалярний добуток векторів

Authored by Світлана Фисун

Mathematics

10th Grade

Used 6+ times

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12 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Скалярним добутком векторів є

число

вектор

координати векторів

інша відповідь

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Якщо вектори перпендикулярні, то скалярний добуток векторів дорівнює

визначити неможливо

-1

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$Відомо,що\ \left|\overrightarrow{\ a}\right|=5,\ а\ \left|\overrightarrow{\ c}\right|=2.$ Чи може скалярний добуток цих векторів дорівнювати 9,7

так

ні

визначити неможливо

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$Дано\ вектор\ \overrightarrow{АС}\left(5;-1;10\right).$ Знайдіть його модуль.

$\sqrt{126}$

$\sqrt{124}$

$\sqrt{16}$

$\sqrt{14}$

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Знайти координати вектора $\overrightarrow{СD}$ , якщо С(5; - 4; 2), D(-3; 2; 1)

(8; - 6; 1)

(-8; 6; - 1)

(2; - 2; 1)

(-2; 2; - 1)

(1;1;1,5)

MULTIPLE CHOICE QUESTION

1 min • 1 pt

$\overrightarrow{p\ }\left(5;\ m;\ -20\right),\ \overrightarrow{s\ }\left(3;\ 6;-12\right)$
При яких значеннях m дані вектори колінеарні

-10

0,6

інша відповідь

FILL IN THE BLANKS QUESTION

2 mins • 1 pt

$Дано\ вектори\ \overrightarrow{n\ }\left(-4;2;-5\right)\ i\ \overrightarrow{n\ }\left(-2;\ -2;3\right).$ Знайдіть скалярний добуток цих векторів. Відповідь записати числом без пробілів

(a)

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Модуль вектора $\overrightarrow{d\ }\left(2;\ y;-6\right)$ дорівнює 7. Якому значенню може дорівнювати $y$

інша відповідь

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Знайдіть модуль вектора $\frac{1}{2}\ \overrightarrow{с\ },$ якщо $\overrightarrow{с\ }\left(-4;2;6\right)$

$\sqrt{14}$

$\sqrt{6}$

$\sqrt{56}$

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Скалярний добуток векторів

Скалярним добутком векторів є

Якщо вектори перпендикулярні, то скалярний добуток векторів дорівнює

Дано вектор АС→(5;−1;10).Дано\ вектор\ \overrightarrow{АС}\left(5;-1;10\right).Дано вектор АС(5;−1;10). Знайдіть його модуль.

Знайти координати вектора СD→\overrightarrow{СD}СD , якщо С(5; - 4; 2), D(-3; 2; 1)

p →(5; m; −20), s →(3; 6;−12)\overrightarrow{p\ }\left(5;\ m;\ -20\right),\ \overrightarrow{s\ }\left(3;\ 6;-12\right)p ​(5; m; −20), s (3; 6;−12) При яких значеннях m дані вектори колінеарні

Модуль вектора d →(2; y;−6)\overrightarrow{d\ }\left(2;\ y;-6\right)d (2; y;−6) дорівнює 7. Якому значенню може дорівнювати yyy

Знайдіть модуль вектора 12 с →,\frac{1}{2}\ \overrightarrow{с\ },21​ с , якщо с →(−4;2;6)\overrightarrow{с\ }\left(-4;2;6\right)с (−4;2;6)

Дано q̅=k⋅а̅. Укажіть значення k, якщо а̅ (−2; 8;−4) і q̅(4;−16; 8)

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$Дано\ вектор\ \overrightarrow{АС}\left(5;-1;10\right).$ Знайдіть його модуль.

Знайти координати вектора $\overrightarrow{СD}$ , якщо С(5; - 4; 2), D(-3; 2; 1)

$\overrightarrow{p\ }\left(5;\ m;\ -20\right),\ \overrightarrow{s\ }\left(3;\ 6;-12\right)$
При яких значеннях m дані вектори колінеарні

Модуль вектора $\overrightarrow{d\ }\left(2;\ y;-6\right)$ дорівнює 7. Якому значенню може дорівнювати $y$

Знайдіть модуль вектора $\frac{1}{2}\ \overrightarrow{с\ },$ якщо $\overrightarrow{с\ }\left(-4;2;6\right)$