Function Repository Resource:

# BinormalVector

Compute the binormal vector of a curve

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["BinormalVector"][c,t] computes the binormal vector of curve c parametrized by t.

## Details and Options

The binormal vector is the cross product of the tangent vector and the normal vector.

## Examples

### Basic Examples (2)

Consider the curve:

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The binormal vector:

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### Scope (2)

Use a helix:

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The binormal vector:

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Calculate the normal vector using the resource function NormalVector:

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The normal vector is the cross product of the binormal vector and the tangent vector. Check this using the previous computation along with the resource function TangentVector:

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The binormal surface associated to a curve is generated by its binormal vector field. It can be computed with the resource function BinormalSurface:

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Check this:

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Combine the binormal surface with the helix curve:

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### Properties and Relations (7)

Define a unit speed helix:

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Its binormal vector:

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The derivative of the binormal vector:

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The torsion, via the resource function CurveTorsion:

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The normal vector, via the resource function NormalVector:

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The torsion multiplied by the normal is the derivative of the binormal:

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Using FrenetSerretSystem, the binormal vector is the last element of the second List:

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Enrique Zeleny

## Version History

• 2.0.0 – 30 April 2020
• 1.0.0 – 28 April 2020