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Thought-Process to Discover Knowledge

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summary of this topic

Properties of Dot Product

Properties of Dot Product

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 »  Modulus of dot product is less than or equal to modulus of the vectors

    →  `|vec p cdot vec q| <= |vec p| |vec q|`

Property of Modulus in dot product

plain and simple summary

nub

plain and simple summary

nub

dummy

 •  Modulus of dot product is less than or equal to the product of modulus of the vectors.

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 property of modulus in vector dot product.


Keep tapping on the content to continue learning.
Starting on learning "Property of Modulus in dot product". ;; In this page, you will learn about the property of modulus in vector dot product.

What is the modulus of dot product `| vec p cdot vec q |`?

  • `=|p| xx |q|`
  • `<=|p| xx |q|`
  • `>=|p| xx |q|`

The answer is '`<=|p| xx |q|`'.
`vec p cdot vec q = |p||q|cos theta`
`| cos theta |<= 1`, so
`|p||q|cos theta <= |p||q|`
`| vec p cdot vec q |<=|p| xx |q|`

The same can be understood with geometrical meaning as given in figure. vector dot product no cancellation `vec q = vec a + vec b`
`|vec q| >= |vec a|`
`|vec p cdot vec q | = |p||a|`
`|vec p cdot vec q | <= |p||q|`

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Modulus Property of Dot Product: For any vectors `vec p` and `vec q`,
`|vec p cdot vec q | <= |p||q|`



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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What is the modulus of dot product vector p dot vector q?
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The answer is "less than equal magnitude p multiplied magnitude q". vector p dot vector q = magnitude p multiplied magnitude q cos theta. ;; magnitude of cos theta less than or equal 1.
The same can be understood with geometrical meaning as given in figure.
Modulus of dot product is less than or equal to the product of modulus of the vectors.
Modulus Property of Dot Product: For any vectors p and q ;; magnitude of, vector p dot vector q ; less than or equal; magnitude of vector p multiplied magnitude of vector q

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