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|`