Orthogonal space-like vectors.

In summary, orthogonal space-like vectors are two perpendicular vectors in a three-dimensional space that are represented using the dot product or cross product. They have various applications in mathematics and physics, including vector calculus and mechanics. They can have different magnitudes as long as they are perpendicular to each other, and their orthogonality can be determined by their dot product, cross product, or angle between them.
  • #1
Felpudio
3
0
Hey, I read that if a four-vector is 'four-orthogonal' to a time-like four vector then it must be space-like. I showed this quite easily.

I also read that a space-like vector can be orthogonal to another space-like vector, but can't seem to prove it. I wondered if someone could help me.
 
Physics news on Phys.org
  • #2
Take one vector pointing along the x-axis and the other pointing along the y-axis.
 

FAQ: Orthogonal space-like vectors.

1. What are orthogonal space-like vectors?

Orthogonal space-like vectors are two vectors in a three-dimensional space that are perpendicular to each other and do not intersect at any point. They are also known as perpendicular or right-angle vectors.

2. How are orthogonal space-like vectors represented?

Orthogonal space-like vectors are usually represented using the dot product or the cross product of two vectors. The dot product results in a scalar value while the cross product results in a vector that is perpendicular to both the original vectors.

3. What is the importance of orthogonal space-like vectors in mathematics and physics?

Orthogonal space-like vectors play a crucial role in many mathematical and physical concepts. For example, they are used in vector calculus, linear algebra, and mechanics. In physics, they are used to represent forces, velocities, and accelerations in a three-dimensional space.

4. Can orthogonal space-like vectors have different magnitudes?

Yes, orthogonal space-like vectors can have different magnitudes as long as they are perpendicular to each other. The magnitude of a vector refers to its length or size, while the direction refers to its orientation in space. Therefore, two vectors can have different magnitudes but still be orthogonal as long as their directions are perpendicular.

5. How can we determine if two vectors are orthogonal space-like vectors?

To determine if two vectors are orthogonal space-like vectors, we can use the dot product or the cross product. If the dot product of two vectors is equal to 0, then they are orthogonal. Similarly, if the cross product of two vectors results in a zero vector, then they are also orthogonal. Another way is to calculate the angle between the two vectors. If the angle is 90 degrees, then they are orthogonal.

Similar threads

B Why is "time orthogonal to space" in inertial reference frames?
2
Replies
69
Views
4K
B Orthogonality in Minkowski Spacetime: Meaning & Visualization
Replies
14
Views
3K
I Synchronous Reference Frame: Definition and Usage
Replies
16
Views
2K
I Understand 4-Vectors & Spacetime: Hartle Gravity Chapter 5
Replies
4
Views
2K
I About global inertial frame in GR - revisited
2
Replies
57
Views
3K
I Why is Number-Flux Four-Vector Frame-Independent?
Replies
4
Views
1K
I Proof that two timelike vectors cannot be orthogonal
Replies
9
Views
3K
I Pullback & orthogonal projector
Replies
2
Views
513
B How Can Time Derivatives Be Taken in GR and SR with Orthogonal Basis Vectors?
Replies
29
Views
3K
A Orthogonal spacelike and timelike vectors and inertial frames
Replies
22
Views
4K

Hot Threads

Recent Insights

Back
Top