Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

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.continue

In this page, you will learn that the vector dot product is not associative.

click on the content to continue..

What is associative property of an operator `***`?associative property illustration

  • `(x *** y) *** z = x *** (y *** z)`
  • `(x *** y) *** z = x *** (y *** z)`
  • `x *** y = y *** x`
  • `x *** y = - y *** x`

The answer is '`(x *** y) *** z = x *** (y *** z)`'. In the left hand side of the equation, `y` is associated with `x` first, where in the right hand side, y is associated with `z` first.

Dot product cannot be considered for associative property. Consider the two `(vec p cdot vec q)` and `vec r`. The first term in parenthesis is a scalar and the second term is a vector.

The dot product is not defined between a scalar and a vector.

 •  Dot product is not associative.

Not Associative: For any vector `vec p, vec q, vec r in bbb V`
`(vec p cdot vec q) vec r != vec p (vec q cdot vec r)`

Solved Exercise Problem:

Consider `(vec x cdot vec y) vec z = vec p (vec q cdot vec z)`. Can the vector `vec z` be canceled on either side of the equation?

  • Yes
  • No
  • No

The answer is 'No'. The `vec z` can be canceled in `(vec x cdot vec y) vec z = (vec p cdot vec q) vec z`. Since associative property is not defined for dot product, the equation given in the question can not be equivalently expressed in this form.

slide-show version coming soon