Vektor satuan dari p → = 2 i − 3 j \overrightarrow{p}\ =2i-3j p <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"> = 2 i − 3 j adalah . . . . .

1 13 ( 2 i − 3 j ) \frac{1}{\sqrt{13}}(2i-3j) 1 3 <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"> 1 ( 2 i − 3 j )

1 5 ( 2 i − 3 j ) \frac{1}{\sqrt{5}}(2i-3j) 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"> 1 ( 2 i − 3 j )

1 10 ( 2 i − 3 j ) \frac{1}{\sqrt{10}}(2i-3j) 1 0 <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"> 1 ( 2 i − 3 j )

4 10 ( 2 i − 3 j ) \frac{4}{\sqrt{10}}(2i-3j) 1 0 <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"> 4 ( 2 i − 3 j )

1 17 ( 2 i − 3 j ) \frac{1}{\sqrt{17}}(2i-3j) 1 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"> 1 ( 2 i − 3 j )

D i k e t a h u i a ⃗ = 2 i + 5 j + 4 k Diketahui\ a⃗=2i+5j+4k D i k e t a h u i a ⃗ = 2 i + 5 j + 4 k b ⃗ = − i + 3 j + 7 k d a n b⃗=-i+3j+7k\ dan b ⃗ = − i + 3 j + 7 k d a n c ⃗ = 5 i − 2 j − k T e n t u k a n a ⃗ + b ⃗ ! c⃗=5i-2j-k\ Tentukan\ a⃗+b⃗! c ⃗ = 5 i − 2 j − k T e n t u k a n a ⃗ + b ⃗ !

i ‾ + 8 j ‾ + 11 k ‾ \overline{i}+8\overline{j}+11\overline{k} i + 8 j + 1 1 k

3 i ‾ + 8 j ‾ + 11 k ‾ 3\overline{i}+8\overline{j}+11\overline{k} 3 i + 8 j + 1 1 k

3 i ‾ − 8 j ‾ + 11 k ‾ 3\overline{i}-8\overline{j}+11\overline{k} 3 i − 8 j + 1 1 k

i ‾ − 8 j ‾ + 11 k ‾ \overline{i}-8\overline{j}+11\overline{k} i − 8 j + 1 1 k

− i ‾ + 8 j ‾ + 11 k ‾ -\overline{i}+8\overline{j}+11\overline{k} − i + 8 j + 1 1 k

D i k e t a h u i a ⃗ = 2 i + 5 j + 4 k Diketahui\ a⃗=2i+5j+4k D i k e t a h u i a ⃗ = 2 i + 5 j + 4 k b ⃗ = − i + 3 j + 7 k d a n b⃗=-i+3j+7k\ dan\ b ⃗ = − i + 3 j + 7 k d a n c ⃗ = 5 i − 2 j − k T e n t u k a n a ⃗ − b ⃗ + c ⃗ ! c⃗=5i-2j-k\ Tentukan\ a⃗-b⃗+c⃗! c ⃗ = 5 i − 2 j − k T e n t u k a n a ⃗ − b ⃗ + c ⃗ !

( 8 , 0 , − 4 ) \left(8,0,-4\right) ( 8 , 0 , − 4 )

( − 8 , 0 , − 4 ) \left(-8,0,-4\right) ( − 8 , 0 , − 4 )

( 6 , 0 , − 4 ) \left(6,0,-4\right) ( 6 , 0 , − 4 )

( − 6 , 0 , − 4 ) \left(-6,0,-4\right) ( − 6 , 0 , − 4 )

( 6 , 0 , 4 ) \left(6,0,4\right) ( 6 , 0 , 4 )

Proyeksi vektor orthogonal vektor a ‾ = 2 i ‾ − 6 j ‾ + 8 k ‾ \overline{a}=2\overline{i}-6\overline{j}+8\overline{k} a = 2 i − 6 j + 8 k pada vektor b ‾ = 3 i ‾ − j ‾ + 2 k ‾ \overline{b}=3\overline{i}-\overline{j}+2\overline{k} b = 3 i − j + 2 k adalah...

6 i ‾ − 2 j ‾ + 4 k ‾ 6\overline{i}-2\overline{j}+4\overline{k} 6 i − 2 j + 4 k

3 i ‾ − j ‾ + 2 k ‾ 3\overline{i}-\overline{j}+2\overline{k} 3 i − j + 2 k

− 3 i ‾ + j ‾ − 2 k ‾ -3\overline{i}+\overline{j}-2\overline{k} − 3 i + j − 2 k

3 2 i ‾ − 1 2 j ‾ + k ‾ \frac{3}{2}\overline{i}-\frac{1}{2}\overline{j}+\overline{k} 2 3 i − 2 1 j + k

− 6 i ‾ + 2 j ‾ − 4 k ‾ -6\overline{i}+2\overline{j}-4\overline{k} − 6 i + 2 j − 4 k

Diketahui segitiga ABC dengan titik A(-2,3,1), B(3,-1,2) dan C(2,1,-3). Jika u ‾ \overline{u} u mewakili A B ‾ \overline{AB} A B dan v ‾ \overline{v} v mewakili A C ‾ \overline{AC} A C , maka vektor proyeksi u ‾ p a d a v ‾ \overline{u}\ pada\ \overline{v} u p a d a v adalah...

8 3 i ‾ − 4 3 j ‾ − 8 3 k ‾ \frac{8}{3}\overline{i}-\frac{4}{3}\overline{j}-\frac{8}{3}\overline{k} 3 8 i − 3 4 j − 3 8 k

− 3 2 i ‾ + 2 j ‾ − 1 2 k ‾ -\frac{3}{2}\overline{i}+2\overline{j}-\frac{1}{2}\overline{k} − 2 3 i + 2 j − 2 1 k

3 2 i ‾ − 2 j ‾ + 1 2 k ‾ \frac{3}{2}\overline{i}-2\overline{j}+\frac{1}{2}\overline{k} 2 3 i − 2 j + 2 1 k

− 8 3 i ‾ + 4 3 j ‾ + 8 3 k ‾ -\frac{8}{3}\overline{i}+\frac{4}{3}\overline{j}+\frac{8}{3}\overline{k} − 3 8 i + 3 4 j + 3 8 k

4 3 i ‾ − 2 3 j ‾ − 4 3 k ‾ \frac{4}{3}\overline{i}-\frac{2}{3}\overline{j}-\frac{4}{3}\overline{k} 3 4 i − 3 2 j − 3 4 k

Diketahui vektor a ‾ = 4 i ‾ − 2 j ‾ + 2 k ‾ \overline{a}=4\overline{i}-2\overline{j}+2\overline{k} a = 4 i − 2 j + 2 k dan vektor b ‾ = 2 i ‾ − 6 j ‾ + 4 k ‾ \overline{b}=2\overline{i}-6\overline{j}+4\overline{k} b = 2 i − 6 j + 4 k . Proyeksi vektor ortogonal vektor a ‾ \overline{a} a pada vektor b ‾ \overline{b} b adalah...

i ‾ − 3 j ‾ + 2 k ‾ \overline{i}-3\overline{j}+2\overline{k} i − 3 j + 2 k

i ‾ − j ‾ + k ‾ \overline{i}-\overline{j}+\overline{k} i − j + k

i ‾ − 4 j ‾ + 4 k ‾ \overline{i}-4\overline{j}+4\overline{k} i − 4 j + 4 k

2 i ‾ − j ‾ + k ‾ 2\overline{i}-\overline{j}+\overline{k} 2 i − j + k

6 i ‾ − 8 j ‾ + 6 k ‾ 6\overline{i}-8\overline{j}+6\overline{k} 6 i − 8 j + 6 k

Latihan soal Vektor

Authored by Dewi Ferina

Mathematics

11th Grade

Used 7+ times

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Jika vektor a = 12 i + 5 k .

Maka panjang vektor a adalah ...

|a| = 11

|a| = 13

|a| = 15

|a| = 17

|a| = 19

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Diketahui koordinat titik K(2,3) dan Titik L(-3,7). Vektor KL adalah .....

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Diketahui vektor pada R3 berikut:
a = 8 i - 4 j + 3 k
b = 3 i - 2 j
c = - i - 5 j + 7 k

Hasil dari 2a - b + 3c adalah ...

13 i + 4 j + 29 k

13 i - 26 j + 29 k

13 i + 26 j + 25 k

10 i + 9 j + 27 k

10 i -21 j + 27 k

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

panjang vektor $\overrightarrow{a\ }=-10i+24j$ adalah……

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$Diketahui\ a⃗=i+2j+2k,$ $b⃗=-3i-j-2k.\ Tentukan\ a⃗.b⃗!$

$-9$

$9$

$1$

$-1$

$-6$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$Diketahui\ a⃗=i+2j+k,$
$b⃗=i-2j-k.\ Tentukan\ a⃗.b⃗!$

$-6$

$-4$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Jika a dan b membentuk sudut $60\degree$ dan |a|=4 , |b|=3. maka hasil dari $\overrightarrow{a}\cdot\overrightarrow{b}$ adalah...

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Diketahui $\overrightarrow{a}=-5i+2j,\ \overrightarrow{b}=-3i+2j$ dan $\overrightarrow{c}=3i-7j$ . Maka nilai $3\overrightarrow{c}-\overrightarrow{a}+2\overrightarrow{b}$ adalah . . . . .

$8i-19j$

$8i+19j$

$-8i-19j$

$-8i+19j$

$8i-19j$

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Vektor satuan dari $\overrightarrow{p}\ =2i-3j$ adalah . . . . .

$\frac{1}{\sqrt{13}}(2i-3j)$

$\frac{1}{\sqrt{5}}(2i-3j)$

$\frac{1}{\sqrt{10}}(2i-3j)$

$\frac{4}{\sqrt{10}}(2i-3j)$

$\frac{1}{\sqrt{17}}(2i-3j)$

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Latihan soal Vektor

Jika vektor a = 12 i + 5 k . ﻿Maka panjang vektor a adalah ...

Diketahui koordinat titik K(2,3) dan Titik L(-3,7). Vektor KL adalah .....

Diketahui vektor pada R3 berikut: a = 8 i - 4 j + 3 kb = 3 i - 2 jc = - i - 5 j + 7 kHasil dari 2a - b + 3c adalah ...

panjang vektor a →=−10i+24j\overrightarrow{a\ }=-10i+24ja =−10i+24j adalah……

Diketahui a⃗=i+2j+2k,Diketahui\ a⃗=i+2j+2k,Diketahui a⃗=i+2j+2k, b⃗=−3i−j−2k. Tentukan a⃗.b⃗!b⃗=-3i-j-2k.\ Tentukan\ a⃗.b⃗!b⃗=−3i−j−2k. Tentukan a⃗.b⃗!

Diketahui a⃗=i+2j+k,Diketahui\ a⃗=i+2j+k,Diketahui a⃗=i+2j+k, b⃗=i−2j−k. Tentukan a⃗.b⃗!b⃗=i-2j-k.\ Tentukan\ a⃗.b⃗!b⃗=i−2j−k. Tentukan a⃗.b⃗!

Jika a dan b membentuk sudut 60°60\degree60° dan |a|=4 , |b|=3. maka hasil dari a→⋅b→\overrightarrow{a}\cdot\overrightarrow{b}a⋅b adalah...

A (0,2) dan B (5,3) maka 3A - 2B = ...

Diketahui a→=−5i+2j, b→=−3i+2j\overrightarrow{a}=-5i+2j,\ \overrightarrow{b}=-3i+2ja=−5i+2j, b=−3i+2j dan c→=3i−7j\overrightarrow{c}=3i-7jc=3i−7j . Maka nilai 3c→−a→+2b→3\overrightarrow{c}-\overrightarrow{a}+2\overrightarrow{b}3c−a+2b adalah . . . . .

Vektor satuan dari p→ =2i−3j\overrightarrow{p}\ =2i-3jp​ =2i−3j adalah . . . . .

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Discover more resources for Mathematics

Jika vektor a = 12 i + 5 k .

Maka panjang vektor a adalah ...

Diketahui vektor pada R3 berikut:
a = 8 i - 4 j + 3 k
b = 3 i - 2 j
c = - i - 5 j + 7 k

Hasil dari 2a - b + 3c adalah ...

panjang vektor $\overrightarrow{a\ }=-10i+24j$ adalah……

$Diketahui\ a⃗=i+2j+2k,$ $b⃗=-3i-j-2k.\ Tentukan\ a⃗.b⃗!$

$Diketahui\ a⃗=i+2j+k,$
$b⃗=i-2j-k.\ Tentukan\ a⃗.b⃗!$

Jika a dan b membentuk sudut $60\degree$ dan |a|=4 , |b|=3. maka hasil dari $\overrightarrow{a}\cdot\overrightarrow{b}$ adalah...

A (0,2) dan B (5,3) maka
3A - 2B = ...

Diketahui $\overrightarrow{a}=-5i+2j,\ \overrightarrow{b}=-3i+2j$ dan $\overrightarrow{c}=3i-7j$ . Maka nilai $3\overrightarrow{c}-\overrightarrow{a}+2\overrightarrow{b}$ adalah . . . . .

Vektor satuan dari $\overrightarrow{p}\ =2i-3j$ adalah . . . . .