__maths__>__Properties of Vector Arithmetics__>__Properties of Vector Addition__### Magnitude Property of Vector Addition

In this page, relation between magnitude of vectors and the magnitude of sum of the vectors is explained.

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Triangular law of vector addition states that the “Two vectors form a triangle with the sum as the third side of the triangle”. Using the results learned in geometry: Sum of length of any two sides of a triangle is, which of the following?

- greater than the third side
- greater than the third side
- equal to the third side
- less than the third side

The answer is 'Greater than the third side'. It is noted that the length of sides of the triangle are magnitudes of the vectors.

• magnitude of sum is less than or equal to sum of magnitudes - Magnitude property of Addition.

**Magnitude property: **For any vector `vec a, vec b in bbb V`

`|vec a+vec b|<=|vec a|+|vec b|`

*Solved Exercise Problem: *

Given that the magnitudes of two collinear vectors are `2.4` and `4.2`, what would be the magnitude of the sum of the two vectors?

- `=6.6`
- `=6.6`
- `!=6.6`
- `<=6.6`
- `>=6.6`

The answer is '`=6.6`'. The vectors are collinear and so, the vectors are in the same direction. In that case, the sum of magnitude equals magnitude of sum.

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