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Thought-Process to Discover Knowledge

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maths >  Properties of Vector Arithmetics >  Properties 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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