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.

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## Glossary

### magnitude

A measure of the size of a mathematical object

### vector

A mathematical object with magnitude and direction.

**Full Glossary List**

More in this topic

1 Exam Question

2 Exam Question

3 Exam Question

4 Magnitude 4

5 Exam Question

6 2D add and subtract

7 Intersection with a circle

8 Distance between two points

9 Exam Question

10 Exam Question

11 Exam Question

12 Exam Question

13 Exam Question

14 Exam Question

15 2D add and subtract 2

16 Exam Question

17 Exam Question

18 3D add and subtract

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 Exam Question

53 Perpendicular vectors

54 Perpendicular vectors 2

55 Exam Question

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