Calculus 3 : Binormal Vectors

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #1 : Binormal Vectors

Find the binormal vector of .

Possible Answers:

Does not exist.

Correct answer:

Explanation:

To find the binormal vector, you must first find the unit tangent vector, then the unit normal vector.  

The equation for the unit tangent vector, ,  is

where  is the vector and  is the magnitude of the vector.

The equation for the unit normal vector,,  is 

where  is the derivative of the unit tangent vector and  is the magnitude of the derivative of the unit vector.

The binormal vector is the cross product of unit tangent and unit normal vectors, or

 

For this problem

 

Example Question #2 : Binormal Vectors

Find the binormal vector of .

Possible Answers:

Does not exist

Correct answer:

Explanation:

To find the binormal vector, you must first find the unit tangent vector, then the unit normal vector.  

The equation for the unit tangent vector, ,  is

where  is the vector and  is the magnitude of the vector.

The equation for the unit normal vector,,  is 

where  is the derivative of the unit tangent vector and  is the magnitude of the derivative of the unit vector.

 

For this problem

Example Question #3 : Binormal Vectors

Find the binormal vector for:

Possible Answers:

Correct answer:

Explanation:

The binormal vector is defined as

Where T(t) (the tangent vector) and N(t) (the normal vector) are:

and

The binormal vector is:

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