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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 Dot Product

Dot Product : No Multiplicative Identity

In this page, you will learn that the vector dot product does not have multiplicative identity.



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What does 'identical' mean?

  • same; similar; alike
  • same; similar; alike
  • different; mismatch

The answer is 'same; similar; alike'

What is the multiplicative identity in real numbers - number system?

  • `1`
  • `1`
  • `0`
  • `-1`

The answer is '`1`'.

For any real number `a`, `a xx 1 = a`, so `1` is the multiplicative identity in real numbers.

Given `vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`, is there a vector `vec r` such that `vec p cdot vec r = vec p`?

 •  No multiplicative identity for Dot Product.

Dot Product does not have an Multiplicative Identity: For any vector `vec p in bbb V`, there is no other vector such that dot product between them is `vec p`.

                            
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