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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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In this page, vector additive inverse is explained.

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What does 'inverse' mean?

  • same; identical; similar
  • opposite; converse
  • opposite; converse

The answer is 'opposite; converse'.

Consider two vectors `vec a = 1.1i-2j` and `vec b = -1.1i+2j`. What will be `vec a+vec b`?

  • the additive identity
  • `vec 0`
  • `0i+0j`
  • all the above
  • all the above

The answer is 'All the above'. For any vector `vec a` there is an inverse `-vec a`, and when these are added the sum is additive identity `vec 0`.

 •  negative of a vector - Additive inverse

Additive Inverse: For any vector `vec a in bbb V` there is an additive inverse vector `-vec a in bbb V` such that
`vec a+(-vec a)=vec 0`

Solved Exercise Problem:

A person A is pulling an object with force `vec f`. But the object is not moving because another person B is also applying force canceling the force by Person A. What is the force with which person B pulling?

  • `-vec f`
  • `-vec f`
  • `vec f cos90^@`
  • `vec f sin90^@`
  • `vec f tan90^@`

The answer is '`-vec f`'

slide-show version coming soon