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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.
mathsProperties of Vector ArithmeticsProperties of Dot Product

### Dot Product : No Multiplicative Inverse

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

click on the content to continue..

What does 'inverse' mean?

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

For two vectors vec p and vec q, the vector dot product is given by multiplication of
•  magnitude of one vector and
•  the magnitude of the component of second vector in parallel to the first vector

vec p cdot vec q = |p| |a|
where |a| is the component of vec q in the direction of vec p.

Given vec p cdot vec q and vec p can vec q be calculated?

What is division?

• inverse of multiplication
• inverse of multiplication
• does not have any relation to multiplication

The answer is 'inverse of multiplication'.

Since dot product is not invertible, the inverse of dot product -- a division -- is not defined.

•  Dot product is not invertible - No multiplicative inverse and no definition of division.

Dot Product - No Multiplicative Inverse: For any vector vec p, vec q in bbb V it is not possible to calculate vec q using the values vec p and vec p cdot vec q.

slide-show version coming soon