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Thought-Process to Discover Knowledge

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mathsVector AlgebraProperties of Cross Product

Property of Modulus in cross product

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



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What is the modulus of cross product `| vec p xx vec q |`?

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

The answer is '`<=|p| xx |q|`'.
`vec p xx vec q = |p||q|sin theta hat n`
`| sin theta |<= 1`, so
`|p||q|sin theta <= |p||q|`
`| vec p xx vec q |<=|p| xx |q|`

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

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

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

                            
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