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Thought-Process to Discover Knowledge

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  nub,

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summary of this topic

Properties of Dot Product

Properties of Dot Product

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 »  vector dot product is NOT associative
    →  `vec p cdot (vec q cdot vec r) ` ` != (vec p cdot vec q) cdot vec r`

Not Associative

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Dot product is not associative.

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 dot product is not associative.


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

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

  • `(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.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

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)`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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

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.

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What is associative property of an operator star?
1
2
3
The answer is "x star y, star z = x star, y star z". In the left hand side of the equation, y is associated with x first, where as in the right hand side, y is associated with z first.
Dot product cannot be considered for associative property. Consider the two, vector p dot vector q and vector 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 vectors p, q, r in vector space v; vector p dot vector q, multiplied vector r; not equals ; vector p multiplied, vector q dot vector r.
Consider vector x dot vector y, vector z = vector p, vector q dot vector z. Can the vector z be canceled on either side of the equation?
1
2
The answer is "No". The vector z can be canceled in vector x dot vector y, multiplied vector z = vector p dot vector q multiplied vector z. ;; Since associative property is not defined for dot product, the equation given in the question can not be equivalently expressed in this form.

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