The magnitude, or size, of a vector
a\underline{i}+b\underline{j} in 2 dimensions is
found by the formula: \sqrt{(a^2+b^2)}

The magnitude, or size, of a vector
a\underline{i}+b\underline{j}+c\underline{k} in 3
dimensions is found by the formula: \sqrt{(a^2+b^2+c^2)}

## Summary/Background

The formula for the magnitude of a vector is basically Pythagoras' theorem extended to 3 dimensions.

## Software/Applets used on this page

This page uses

jsMathYou can get a better display of the maths by downloading special TeX fonts from

jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

## Glossary

### magnitude

A measure of the size of a mathematical object

### union

The union of two sets A and B is the set containing all the elements of A and B.

### vector

A mathematical object with magnitude and direction.

**Full Glossary List**

More in this topic

1 2D add and subtract

2 Exam Question

3 Intersection with a circle

4 Distance between two points

5 Exam Question

6 Exam Question

7 Exam Question

8 Exam Question

9 Exam Question

10 Exam Question

11 Exam Question

12 Exam Question

13 Magnitude 4

14 Exam Question

15 Exam Question

16 2D add and subtract 2

17 3D add and subtract

18 Exam Question

19 Multiplication by a scalar 2

20 Sequence O-test

21 Unit vectors

22 Unit vectors 2

23 Unit vectors 3

24 Equations of lines 2

25 Equations of lines

26 Equations of lines 3

27 Equations of lines 4

28 Equations of lines 5

29 Intersecting lines

30 Area of a triangle

31 Area of a triangle 2

32 Vector to cartesian form

33 Exam Question

34 Exam Question

35 Exam Question

36 Exam Question

37 Scalar product

38 Angle between vectors

39 Angle between vectors 2

40 O-test 1

41 Angle between 2D lines

42 O-test 2

43 Angle between 2D lines 2

44 Angle between 3D lines

45 Foot of perpendicular

46 Exam Question

47 Exam Question

48 Exam Question

49 Exam Question

50 Exam Question

51 Exam Question

52 Perpendicular vectors

53 Exam Question

54 Exam Question

55 Perpendicular vectors 2

56 Perpendicular vectors 3

57 Exam Question

58 Exam Question

59 Perpendicular vectors 4

60 Perpendicular lines

61 Perpendicular lines 2

62 O-test 3

63 O-test 4

64 Exam Question

65 Exam Question

66 Exam Question

67 Exam Question

68 Exam Question

69 Exam Question

70 Exam Question

71 Exam Question

72 Exam Question

73 Exam Question

74 Exam Question

75 Collinear points

76 O-test 5

77 Memorise the formulae

78 Diagonals of a parallelogram

79 Extended problem 1

80 Extended problem 2

81 O-test 6

82 O-test 7

83 O-test 8

84 Exam O-test 1

85 Exam O-test 2

86 Exam O-test 3

87 Exam O-test 4

88 Exam O-test 5

89 Exam timed O-test