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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.continue
mathsVector AlgebraProperties of Dot Product

Dot Product: Commutative Property

In this page, you will learn about the commutative property of vector dot product.



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What does 'commute' mean?commutative property illustration

  • to go to and fro on a regular basis
  • to go to and fro on a regular basis
  • different

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

Given the definition of dot product as
`vec p cdot vec q = |vec p||vec q|cos theta`
What is `vec q cdot vec p`?

  • `vec p cdot vec q`
  • `|p||q|cos(theta)`
  • `|p||q|cos(-theta)`
  • all the above
  • all the above

The answer is 'All the above' Note that `cos(-theta) = cos(theta)`.

Given the definition of dot product as
`vec p cdot vec q = p_xq_x+p_yq_y+p_zq_z`
What is `vec q cdot vec p`?

  • `vec p cdot vec q`
  • `q_xp_x+q_yp_y+q_zp_z`
  • `p_xq_x+p_yq_y+p_zq_z`
  • all the above
  • all the above

The answer is 'All the above'

 • Vectors can be swapped in dot product - commutative.

Commutative Property of Dot Product: For any vector `vec p, vec q in bbb V`
`vec p cdot vec q =vec q cdot vec p`

Solved Exercise Problem:

Given that `vec p cdot vec q = 2.1i-1.7j+6k`, find the `vec q cdot vec p`.

  • `-2.1i+1.7j-6k`
  • `2.1i-1.7j+6k`
  • `2.1i-1.7j+6k`
  • `sqrt(2.1^2+1.7^2+6^2)`
  • `2.1^2+1.7^2+6^2`

The answer is '`2.1i-1.7j+6k`' as dot product is commutative.

                            
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