a → ( a 1 ; a 2 ) ; b → ( b 1 ; b 2 ) \overrightarrow{\ a}\left(a_1;a_2\right)\ ;\ \overrightarrow{\ b}\left(b_1;b_2\right) a <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"> ( a 1 ; a 2 ) ; b <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"> ( b 1 ; b 2 ) Hogy számolom ki a skalárszorzatot koordinátákkal?

a 1 ⋅ b 1 + a 2 ⋅ b 2 a_1\cdot b_1+a_2\cdot b_2 a 1 ⋅ b 1 + a 2 ⋅ b 2

a 1 + a 2 + b 1 + b 2 a_1+a_2+b_1+b_2 a 1 + a 2 + b 1 + b 2

a 1 ⋅ a 2 ⋅ b 1 ⋅ b 2 a_1\cdot a_2\cdot b_1\cdot b_2 a 1 ⋅ a 2 ⋅ b 1 ⋅ b 2

a 1 ⋅ a 2 + b 1 ⋅ b 2 a_1\cdot a_2+b_1\cdot b_2 a 1 ⋅ a 2 + b 1 ⋅ b 2

Mi lesz a C D → \overrightarrow{CD} C D <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"> vektor hossza? C D → ( − 5 ; − 6 ) \overrightarrow{CD}\left(-5;-6\right) C D <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 ; − 6 )

61 \sqrt{61} 6 1 <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">

11 \sqrt{11} 1 1 <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">

− 61 \sqrt{-61} − 6 1 <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">

− 11 \sqrt{-11} − 1 1 <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">

Mi lesz az E F → \overrightarrow{EF} E F <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"> vektor hossza, ha E F → ( 6 ; 1 ) \overrightarrow{EF}\left(6;1\right) E F <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"> ( 6 ; 1 ) ?

37 \sqrt{37} 3 7 <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">

35 \sqrt{35} 3 5 <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">

Vektorok a koordinátarendszerben

Presentation

•

Mathematics

•

11th Grade

•

Practice Problem

•

Medium

Rita Rein

Used 7+ times

FREE Resource

3 Slides • 17 Questions

Vektorok a koordinátarendszerben

Multiple Choice

Hogy végzem el a vektorműveleteket koordinátákkal?

A koordinátákkal végzem el rendre.

Simán a koordinátákkal

Az első vektor koordinátáival végzem el, majd a második koordinátáival is.

Az egyik x koordinátáját a másik y koordinátájával fogom össze és fordítva.

Fill in the Blanks

Mi lesz a következő vektorművelet eredménye: $\overrightarrow{\ a}\left(3;4\right);\ \ \overrightarrow{b\ }\left(2;5\right);\ \overrightarrow{a\ }+\overrightarrow{\ b}\$

Type answer...

Fill in the Blanks

Mi lesz a következő vektorművelet eredménye: $\overrightarrow{\ a}\left(3;4\right);\ \ \overrightarrow{b\ }\left(2;5\right);\ \overrightarrow{a\ }-\overrightarrow{\ b}\$

Type answer...

Fill in the Blanks

Mi lesz a következő vektorművelet eredménye: $\overrightarrow{\ a}\left(3;4\right);\ \ \overrightarrow{b\ }\left(2;5\right);\ 2\overrightarrow{a\ }\$

Type answer...

Multiple Choice

$\overrightarrow{\ a}\cdot\overrightarrow{\ b}$

Milyen szorzatnak nevezzük a következő kifejezést:

Két vektor szorzatának

vektoriális szorzat

skaláris szorzat

szorzat

Multiple Choice

Miért skaláris szorzat?

Mert a végeredmény egy vektor.

Mert végeredmény egy szám.

Mert két vektort szorzunk össze.

Mert koordinátákkal is ki tudjuk számolni.

Multiple Choice

Mi a skaláris szorzat helyes képlete a és b vektorok esetén?

Multiple Choice

$\overrightarrow{\ a}\left(a_1;a_2\right)\ ;\ \overrightarrow{\ b}\left(b_1;b_2\right)$ Hogy számolom ki a skalárszorzatot koordinátákkal?

$a_1+a_2+b_1+b_2$

$a_1\cdot a_2\cdot b_1\cdot b_2$

$a_1\cdot a_2+b_1\cdot b_2$

$a_1\cdot b_1+a_2\cdot b_2$

Fill in the Blanks

$\overrightarrow{\ a}\left(1;7\right);\ \overrightarrow{\ b}\left(2;-3\right)$

Mi lesz a skaláris szorzata a következő két vektornak:

Type answer...

Multiple Choice

Mi a helyvektor?

Origóból a pontba mutató vektor

Pontból az origóba mutató vektor

x tengely pozitív felén levő egységvektor

y engely pozitív felén levő egységvektor

$\overrightarrow{AB}$ vektor meghatározása

Figyeld meg az ábrát!

Multiple Choice

Hogy lehet $\overrightarrow{AB}$ vektort kiszámolni?

$\overrightarrow{AB}=\overrightarrow{\ b}-\overrightarrow{\ a}$

Azaz a második pont helyvektorából kivonva az első pont heyvektorát kapom meg az $\overrightarrow{AB}$ vektort.

Multiple Choice

Mi lesz az $\overrightarrow{AB}$ koordinátája, ha A(2;7) és B(3;5)

(1;-2)

(-1;2)

(5;12)

Multiple Choice

Mennyi lesz az a vektor hossza, ha koordinátái: (5;-3)?

25+9

$\sqrt{34}$

$\sqrt{16}=4$

Nincs hossza negatív lenne a gyök alatt

Multiple Choice

Mi lesz a $\overrightarrow{CD}$ , ha C(4;9) és D(-1;3)

(3;6)

(-5;-6)

(5;6)

(3;12)

Multiple Choice

Mi lesz a $\overrightarrow{CD}$ vektor hossza? $\overrightarrow{CD}\left(-5;-6\right)$

$\sqrt{11}$

$\sqrt{61}$

$\sqrt{-61}$

$\sqrt{-11}$

nincs értelme

Fill in the Blanks

Mi lesz az $\overrightarrow{EF}$ vektor, ha E(2;-5); F(8;-4)?

Type answer...

Multiple Choice

Mi lesz az $\overrightarrow{EF}$ vektor hossza, ha $\overrightarrow{EF}\left(6;1\right)$ ?

$37$

$\sqrt{37}$

$\sqrt{35}$

Más

Vektorok a koordinátarendszerben

Show answer

Auto Play

Slide 1 / 20

SLIDE

Similar Resources on Wayground

14 questions

SUDUT PUSAT DAN SUDUT KELILING

Presentation

•

11th Grade

16 questions

Types Fractions

Presentation

•

KG - 12th Grade

17 questions

Multiplying radicals with variables

Presentation

•

10th - 11th Grade

12 questions

Inverse Functions

Presentation

•

11th - 12th Grade

16 questions

Intro to Geometry - Vocab/Basics

Presentation

•

10th Grade

16 questions

Unit 4 Lesson 1 Factoring Quadratic Expressions

Presentation

•

11th Grade

13 questions

Trigonometry-Finding Missing Side

Presentation

•

10th Grade

14 questions

PROGRESIONES ARITMETICAS

Presentation

•

11th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

12 questions

Identify Rigid Transformations

Quiz

•

8th - 12th Grade

10 questions

Complementary, Supplementary, Vertical, and Linear Pairs

Quiz

•

9th - 12th Grade

22 questions

Identify Vertical and Horizontal Translations

Quiz

•

9th - 12th Grade

10 questions

Graphing Inequalities on a Number Line

Quiz

•

9th - 12th Grade

17 questions

Identifying Parallel And Perpendicular Lines

Quiz

•

9th - 12th Grade

18 questions

Integer Operations

Quiz

•

5th - 12th Grade

18 questions

Parallel lines cut by a transversal

Quiz

•

9th - 11th Grade

14 questions

Evaluate Linear Functions and Their Applications

Quiz

•

9th - 12th Grade