. f i n d t h e m a g n i t u d e o f 2 i + 3 j − 3 k find\ the\ magnitude\ of\ \ 2i\ +3j-\sqrt{3}k f i n d t h e m a g n i t u d e o f 2 i + 3 j − 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"> k

22 \sqrt{22} 2 2 <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">

F i n d t h e d i r e c t i o n cos ⁡ i n e o f 3 i − 2 j + 3 k Find\ the\ direction\ \cos ine\ of\ \ 3i-2j+3k F i n d t h e d i r e c t i o n cos i n e o f 3 i − 2 j + 3 k Fin

3 22 , − 2 22 , 3 22 \frac{3}{\sqrt{22}},\frac{-2}{\sqrt{22}},\frac{3}{\sqrt{22}} 2 2 <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"> 3 , 2 2 <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"> − 2 , 2 2 <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"> 3

3 22 , − 2 22 , 3 22 \frac{3}{22},\frac{-2}{22},\frac{3}{22} 2 2 3 , 2 2 − 2 , 2 2 3

3 22 , 2 22 , 3 22 \frac{3}{\sqrt{22}},\frac{2}{\sqrt{22}},\frac{3}{\sqrt{22}} 2 2 <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"> 3 , 2 2 <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"> 2 , 2 2 <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"> 3

− 3 22 , − 2 22 , 3 22 \frac{-3}{\sqrt{22}},\frac{-2}{\sqrt{22}},\frac{3}{\sqrt{22}} 2 2 <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"> − 3 , 2 2 <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"> − 2 , 2 2 <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"> 3

Given the line L: r = a + tb, where a = i+2j+3k and b= 2i -3j + k

a line with direction vector 4i -6j + 2k is parallel to L

a line with direction vector 2i +4j + 6k is parallel to L

a line with direction vector 3i - j + 7k is parallel to L

Given parallel vectors u and v. Answer ALL that apply

their scalar product is either 1 or -1

magnitude of u equals the magnitude of v

The scalar product of u and v is zero, therefore...

vectors u and v are perpendicular

i − j + k i s i-j+k\ is i − j + k i s unit vector in the direction of

i − j + k 3 \frac{i-j+k}{\sqrt{3}} 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"> i − j + k -8

i − j + k 3 \frac{i-j+k}{3} 3 i − j + k

i − j + k 1 \frac{i-j+k}{1} 1 i − j + k

Given parallel vectors u and v. Answer ALL that apply

their scalar product is either 1 or -1

magnitude of u equals the magnitude of v

⋅ \cdot ⋅ the projection of line joining (1,-2.-1) to (3,1,1) on the vector 4 i − 3 j + 12 k 4i-3j+12k 4 i − 3 j + 1 2 k

23 169 \frac{23}{169} 1 6 9 2 3

23 17 \frac{23}{\sqrt{17}} 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"> 2 3

. . . find the moment of a force 4 i − k a b o u t t h e p o i n t 2 i + j − k a c t i n g t h r o u g h i + j + k 4i-k\ about\ the\ point\ 2i+j-k\ acting\ through\ i+j+k 4 i − k a b o u t t h e p o i n t 2 i + j − k a c t i n g t h r o u g h i + j + k

237 \sqrt{237} 2 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">

57 \sqrt{57} 5 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">

vector algebra

Authored by thres vimala

Mathematics

12th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

. $find\ the\ magnitude\ of\ \ 2i\ +3j-\sqrt{3}k$

$\sqrt{22}$

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the magnitude.

square root of 5

Tags

CCSS.HSN.VM.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find the resultant vector.

<9, 15>

<7, 17>

<15, 9>

<11, 13>

Tags

CCSS.HSN.VM.A.1

CCSS.HSN.VM.B.4

CCSS.HSN.VM.C.10

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

How do you know if two vectors are orthogonal?

Their sum is 0.

The dot product is 1.

The angle between them is 0°.

The dot product is 0.

Tags

CCSS.HSN.VM.A.1

CCSS.HSG.GPE.B.5

CCSS.HSG.CO.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$Find\ the\ angle\ between\ the\ vectors\ i-j+k\ and\ -i+j+2k$

49.76°

90°

92.57°

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

$Find\ the\ direction\ \cos ine\ of\ \ 3i-2j+3k$ Fin

$\frac{3}{22},\frac{-2}{22},\frac{3}{22}$

$\frac{3}{\sqrt{22}},\frac{2}{\sqrt{22}},\frac{3}{\sqrt{22}}$

$\frac{3}{\sqrt{22}},\frac{-2}{\sqrt{22}},\frac{3}{\sqrt{22}}$

$\frac{-3}{\sqrt{22}},\frac{-2}{\sqrt{22}},\frac{3}{\sqrt{22}}$

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Vectors a, b, c are defined as:
a = 2i + 5j; b = i - 3j; c = -3i - j. Answer all correct answers

a + b = 3i + 8j

a - b = i + 8j

a + c = -i + 4j

c - b = -5i + 6j

Tags

CCSS.HSN-VM.B.4A

CCSS.HSN-VM.B.4B

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vector algebra

. $find\ the\ magnitude\ of\ \ 2i\ +3j-\sqrt{3}k$

Find the magnitude.

Find the resultant vector.

How do you know if two vectors are orthogonal?

$Find\ the\ angle\ between\ the\ vectors\ i-j+k\ and\ -i+j+2k$

$Find\ the\ direction\ \cos ine\ of\ \ 3i-2j+3k$ Fin

Vectors a, b, c are defined as:
a = 2i + 5j; b = i - 3j; c = -3i - j. Answer all correct answers

Vector a = 2i + 3j - 5k. What is the value of 3a?

Given points A(3, 2, -4) and B(2, 1, -1), so the vector AB is

Given the vector v = 3i -2j +6 k, the magnitude of v is:

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vector algebra

. find the magnitude of 2i +3j−3kfind\ the\ magnitude\ of\ \ 2i\ +3j-\sqrt{3}kfind the magnitude of 2i +3j−3​k

Find the magnitude.

Find the resultant vector.

How do you know if two vectors are orthogonal?

Find the angle between the vectors i−j+k and −i+j+2kFind\ the\ angle\ between\ the\ vectors\ i-j+k\ and\ -i+j+2kFind the angle between the vectors i−j+k and −i+j+2k

Find the direction cos⁡ine of 3i−2j+3kFind\ the\ direction\ \cos ine\ of\ \ 3i-2j+3kFind the direction cosine of 3i−2j+3k Fin

Vectors a, b, c are defined as:a = 2i + 5j; b = i - 3j; c = -3i - j. Answer all correct answers

Vector a = 2i + 3j - 5k. What is the value of 3a?

Given points A(3, 2, -4) and B(2, 1, -1), so the vector AB is

Given the vector v = 3i -2j +6 k, the magnitude of v is:

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. $find\ the\ magnitude\ of\ \ 2i\ +3j-\sqrt{3}k$

$Find\ the\ angle\ between\ the\ vectors\ i-j+k\ and\ -i+j+2k$

$Find\ the\ direction\ \cos ine\ of\ \ 3i-2j+3k$ Fin

Vectors a, b, c are defined as:
a = 2i + 5j; b = i - 3j; c = -3i - j. Answer all correct answers