# How can I determine an orthogonal vector to a given vector in 3D space?

• rocketman123
In summary, the conversation discusses how to find an orthogonal vector to a given vector, as well as how to determine a suitable 'up' and 'horizontal' vector in a directional vector scenario. The proposed solution involves taking the cross product of the directional vector and a predefined up vector, as well as taking the cross product of the horizontal vector and the directional vector to get the proper up vector. However, there is uncertainty about the correctness of this solution and the need for 3d plotting software to verify it.
rocketman123
Hey guys,

Given a vector, ie < -1, 2, 3 > , how does one go about finding a vector which is orthogonal to it?

I also have another vector < x, y ,z > which is the point of origin for the above vector.

In context, I'm given a directional vector from which I need to find an 'up' vector and a 'horizontal' vector. You can see here http://www.cs.auckland.ac.nz/~jli023/images/opengl/pov-ray/viewplaneAnglechanged.jpg - I have a 'look_at' vector and must determine a suitable up and right vector.

I know that to get the right/ horiztonal vector I can just take the cross product between the directional / look at vector and the up vector. However, how to get the up vector confuses me.

A standard up vector is <0 1 0 >. Would it make sense to take the cross product of <0 1 0 > and the direction vector - to get the horizontal vector. And then take the cross product of the horizontal and directional vectors to get the proper up vector? It makes sense to me, however I have no real way of checking if my answer is correct! - I need to find some nice 3d plotting software hehe

Cheers,
Dan

Welcome to PF!

Hi Dan! Welcome to PF!

I'm confused … surely all up vectors are the same?

(and not orthogonal to the 'look at' vector)

## 1. What is an orthogonal vector?

An orthogonal vector is a vector that is perpendicular to another vector, meaning that the angle between the two vectors is 90 degrees. This is also known as being "orthogonal" or "normal".

## 2. Why is finding an orthogonal vector important?

Finding an orthogonal vector is important in many fields of science and mathematics. It allows us to solve problems involving angles, distances, and even forces. It is also a fundamental concept in linear algebra and vector calculus.

## 3. How do you find an orthogonal vector?

To find an orthogonal vector, you can use the dot product or cross product of two given vectors. The dot product of two orthogonal vectors will always be zero, while the cross product of two orthogonal vectors will result in a new vector that is perpendicular to both of the original vectors.

## 4. Can any vector be orthogonal to another vector?

No, not all vectors can be orthogonal to each other. In order for two vectors to be orthogonal, their dot product must be equal to zero. This means that the vectors must have a specific relationship in terms of direction and magnitude in order to be orthogonal.

## 5. How is finding an orthogonal vector used in real-world applications?

Finding orthogonal vectors has many practical applications, such as in computer graphics, engineering, and physics. It is used to calculate angles and distances in 3D space, as well as to solve problems involving forces and motion. It is also used in data compression algorithms and signal processing techniques.

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