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)}
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
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.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AQA A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra | - |
| AQA A2 Maths 2017 | Mechanics | Kinematics | 3D Vectors | - |
| AQA AS Maths 2017 | Mechanics | Vectors | Vector Basics | - |
| AQA AS/A2 Maths 2017 | Mechanics | Vectors | Vector Basics | - |
| CBSE XII (India) | Vectors and 3-D Geometry | Vectors | Types, equal, unit, parallel, collinear | - |
| CCEA A-Level (NI) | C4 | Vectors | Vector algebra | - |
| CIE A-Level (UK) | P1 | Vectors | Vector algebra | - |
| Edexcel A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra | - |
| Edexcel A2 Maths 2017 | Pure Maths | Vectors | 3D Vectors | - |
| Edexcel AS Maths 2017 | Pure Maths | Vectors | Vector Basics | - |
| Edexcel AS/A2 Maths 2017 | Pure Maths | Vectors | Vector Basics | - |
| I.B. Higher Level | 4 | Vectors | Vector algebra | - |
| I.B. Standard Level | 4 | Vectors | Vector algebra | - |
| Methods (UK) | M4 | Vectors | Vector algebra | - |
| OCR A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra | - |
| OCR A2 Maths 2017 | Pure Maths | Vectors | 3D Vectors | - |
| OCR AS Maths 2017 | Pure Maths | Vectors | Vector Basics | - |
| OCR MEI A2 Maths 2017 | Pure Maths | Vectors | 3D Vectors | - |
| OCR MEI AS Maths 2017 | Pure Maths | Vectors | Vector Basics | - |
| OCR-MEI A-Level (UK - Pre-2017) | C4 | Vectors | Vector algebra | - |
| Pre-Calculus (US) | E1 | Vectors | Vector algebra | - |
| Pre-U A-Level (UK) | 6 | Vectors | Vector algebra | - |
| Scottish (Highers + Advanced) | HM3 | Vectors | Vector algebra | - |
| Scottish Highers | M3 | Vectors | Vector algebra | - |
| Universal (all site questions) | V | Vectors | Vector algebra | - |
| WJEC A-Level (Wales) | C4 | Vectors | Vector algebra | - |