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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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mathsVector AlgebraProperties 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”.magnitude property of vector addition 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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