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Thought-Process to Discover Knowledge

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mathsVector AlgebraProperties 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. 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|

slide-show version coming soon