How to Determine Orthogonal Vectors

In summary, the conversation discusses finding out if a vector is orthogonal to a given plane. The speaker has searched for solutions but found different methods. They provide an example and ask for advice on how to solve it. They mention using the formula ax + by + cz = 0 and express uncertainty in working it out. The solution is suggested as forming vectors AB and AC and verifying if the given vector is orthogonal to both.
  • #1
AOXX24
2
0
Hey guys,

I have searched all over the forum but each thread seems to have a different way of solving this problem.

I have changed the values from the coursework question so I can work it out for myself so here is an example one, I hope someone can give me some advice/steps on how to work it out.

Find out whether vector v = [− 3, −5, −4]T is orthogonal to the plane containing points
A(-8,4,5), B(-3,8,4) and C(8,-2-1).

I know what I need to use ax + by + cz = 0, I'm just unsure of how to work it out. :)
 
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  • #2
A vector is orthogonal to a plane if it is orthogonal to two non parallel vectors in that plane.
Form the vectors AB and AC and verify if v is orthogonal to both.
 
  • #3
will do , thank you :)
 

1. What is the definition of orthogonal vectors?

Orthogonal vectors are a pair of vectors that are perpendicular to each other, meaning they form a 90 degree angle. This can also be referred to as being "normal" to each other.

2. How do you determine if two vectors are orthogonal?

To determine if two vectors are orthogonal, you can use the dot product equation: a · b = 0. If the dot product of two vectors is equal to 0, then they are orthogonal.

3. Can any two non-zero vectors be considered orthogonal?

No, in order for two vectors to be considered orthogonal, they must be perpendicular to each other. This means that the dot product of the two vectors must equal 0.

4. What is the geometric significance of orthogonal vectors?

The geometric significance of orthogonal vectors is that they form a basis for a coordinate system. This allows for easier calculations and interpretations of data in multiple dimensions.

5. How are orthogonal vectors used in real-world applications?

Orthogonal vectors are used in various fields, such as engineering, computer graphics, and physics. They are used to represent and manipulate multi-dimensional quantities, and are especially useful for solving problems involving forces and motion.

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