Finding Unit Normal Vector of 2 Vectors

In summary, a unit normal vector is a vector with a magnitude of 1 that is perpendicular to a given vector or surface. It can be found by using the cross product of two given vectors. The unit normal vector can be negative depending on the direction and orientation of the vectors. It is important in various fields of science and engineering. A normal vector, on the other hand, does not have a specific magnitude and is simply perpendicular to a given vector or surface.
  • #1
milan666
13
0

Homework Statement


Im given two vectors and I am told to find theyre unit normal vector.

Homework Equations



a x b

The Attempt at a Solution


I used the cross product of the 2 vectors to find the normal vector, however, it came out to be i + j + k. My question is, is this already a unit vector or do i need to use the equation [tex]\hat{}n[/tex] = n/[tex]\left|n\right|[/tex]?
 
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  • #2
i+j+k is not a unit vector unit vector has magnitude 1 unit vector in the direction of i+j+k is (i+j+k)/3^.5
 
  • #3
Understood, thank youuuuuu.
 

1. What is a unit normal vector?

A unit normal vector is a vector that has a magnitude of 1 and is perpendicular to a given vector or surface. It is also sometimes referred to as a "normal unit vector".

2. How do you find the unit normal vector of two given vectors?

To find the unit normal vector of two given vectors, you can use the cross product (also known as the vector product) of the two vectors. The resulting vector will be perpendicular to both of the original vectors and will have a magnitude of 1.

3. Can the unit normal vector of two vectors be negative?

Yes, the unit normal vector of two vectors can be negative. This will depend on the direction of the vectors and the orientation of the coordinate system being used.

4. Why is it important to find the unit normal vector of two vectors?

Finding the unit normal vector of two vectors is important in many fields of science and engineering. It is commonly used in physics and mechanics to calculate forces and moments, in computer graphics to determine surface normals for shading, and in mathematics to find the equation of a plane.

5. What is the difference between a unit normal vector and a normal vector?

A unit normal vector has a magnitude of 1, while a normal vector does not have a specific magnitude. A normal vector can have any magnitude and is simply a vector that is perpendicular to a given vector or surface.

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