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  nub,

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nub is the simple explanation of the concept.

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summary of this topic

Properties of Cross Product

Properties of Cross Product

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 »  Vector Cross Product is NOT commutative

    →  `vec p xx vec q != vec q xx vec p`

    →  `vec p xx vec q = - vec q xx vec p`

Cross Product : Not Commutative

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  In a cross product if the vectors are swapped, the result is negative of the product. - not 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 that the vector cross product is not commutative.


Keep tapping on the content to continue learning.
Starting on learning, "cross product is not commutative". ;; In this page, you will learn that the vector cross product is not commutative.

What does 'commute' mean?commutative property illustration

  • to go to and fro on a regular basis
  • it does not mean anything

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

Given the definition of cross product as
`vec p xx vec q = |vec p||vec q|sin theta hat n`
What is `vec q xx vec p`?

  • `vec p xx vec q`
  • `|p||q|sin(theta) hat n`
  • `|p||q|sin(-theta) hat n`
  • all the above

The answer is '`|p||q|sin(-theta) hat n`'. The angle traversed from `vec q` to `vec p` is `-theta`.

Given the definition of cross product as
`vec p xx vec q = |(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`
What is `vec q xx vec p`?

  • `-vec p xx vec q`
  • `|(i, j, k),(q_x, q_y, q_z),(p_x, p_y, p_z)|`
  • `-|(i, j, k),(p_x, p_y, p_z),(q_x, q_y, q_z)|`
  • all the above

The answer is 'All the above'

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Not Commutative: For any vector `vec p, vec q in bbb V`
`vec p xx vec q = - vec q xx vec p`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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

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Progress

What does 'commute' mean?
go;fro;regular
to go to and fro on a regular basis
does;not;mean
it does not mean anything
The answer is 'to go to and fro between two places on a regular basis'.
Given the definition of cross product as vector p cross vector q =; magnitude of p, magnitude of q, sine theta, n hat; What is vector q cross vector p?
1
2
3
4
The answer is "magnitude of p, magnitude of q, sine minus theta, n hat". The angle traversed from vector q to vector p is minus theta.
Given the definition of cross product as vector p cross vector q in determinant form; What is vector q cross vector p?
1
2
3
4
The answer is 'All the above'
In a cross product if the vectors are swapped, the result is negative of the product. - not commutative.
Not Commutative: For any vector p, q in vector space v, vector p cross vector q = minus vector q cross vector p.
Given that vector p cross vector q = 2 point 1 i minus 1 point 7 j + 6 k ; find the vector q cross vector p.
1
2
3
4
The answer is "minus 2 point 1 i + 1 point 7 j minus 6 k".

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