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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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### Commutative Property of Vector Addition

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What does 'commute' mean?

• to go to and fro on a regular basis
• to go to and fro on a regular basis
• is it an English word?

The answer is 'to go to and fro between two places on a regular basis'.

Vector addition is the addition of components. The components are real numbers. If the vectors are swapped in a vector addition, will the sum be same?

• the result will be same
• the result will be same
• the result will change

The answer is 'the result will be same'. The real numbers are commutative. The components of vectors are real numbers and so vectors are commutative.

•  Vectors can be swapped in vector addition - commutative.

Commutative Property of Vector Addition: For any vector vec a, vec b in bbb V
vec a+vec b =vec b + vec a

Solved Exercise Problem:

Given that vec p + vec q = 2i-1.2j+.5k, Which one of the following is vec q + vec p?.

• .5i-1.2j+2k
• .5i+2j-1.2k
• 2i-1.2j+.5k
• 2i-1.2j+.5k
• -1.2i+.5j+2k

The answer is '2i-1.2j+.5k', since vector addition is commutative.

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