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mathsVector AlgebraProperties of Cross Product

### Property of Modulus in 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. 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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