### All Calculus 3 Resources

## Example Questions

### Example Question #1 : Binormal Vectors

Find the binormal vector of .

**Possible Answers:**

Does not exist.

**Correct answer:**

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 #1 : Binormal Vectors

Find the binormal vector of .

**Possible Answers:**

Does not exist

**Correct answer:**

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:**

The binormal vector is defined as

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

and

The binormal vector is: