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summary of this topic

Properties of Dot Product

Properties of Dot Product

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 »  vector dot product is commutative
    →  `vec p cdot vec q = vec q cdot vec p`

Commutative Property

plain and simple summary

nub

plain and simple summary

nub

dummy

 • Vectors can be swapped in dot product - commutative.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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


Keep tapping on the content to continue learning.
Starting on learning the "Commutative Property of vector dot product".

What does 'commute' mean?commutative property illustration

  • 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

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

The answer is 'All the above'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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`
  • `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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What does 'commute' mean?
go;fro;regular;basis
to go to and fro on a regular basis
different
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 ?
1
2
3
4
The answer is "All the above". Note that cos of minus theta = cos theta.
Given the definition of dot product as vector p dot vector q = p x q x + p y q y + p z q z ;; What is vector q dot vector p?
1
2
3
4
The answer is 'All the above'
Vectors can be swapped in dot product - commutative.
Commutative Property of Dot Product: For any vector p, q in vector space v ;; vector p dot vector q = vector q dot vector p.
Given that vector p dot vector q = 2 point 1 i minus 1 point 7 j + 6 k ; find the vector q dot vector p.
1
2
3
4
The answer is "2 point 1 i minus 1 point 7 j plus 6 k ", as dot product is commutative.

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