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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.

Read in the blogs more about the unique learning experience at nubtrek.

### 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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