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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
mathsProperties of Vector ArithmeticsProperties of Dot Product

Property of Modulus in dot product

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



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

  • `=|p| xx |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|`

 •  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 `vec p` and `vec q`,
`|vec p cdot vec q | <= |p||q|`

                            
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