__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. `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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