Transitive Property with Orthogonal Vectors?

In summary, if x1 is orthogonal to x2 and x2 is orthogonal to x3, it is not necessarily true that x1 is orthogonal to x3. This can be seen by imagining a geometric example and trying to prove it algebraically.
  • #1
georgetown13
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0

Homework Statement



Let x1, x2, and x3 be vectors in R^3. If x1 is orthogonal to x2 and x2 is orthogonal to x3, is it necessarily true that x1 is orthogonal to x3?


Homework Equations



I know that if x1 is orthogonal to x2 and x2 is orthogonal to x3, then...

(x1)^T*x2=0
(x2)^T*x3=0


The Attempt at a Solution



I think that the answer would be no. I can imagine it geometrically, but I'm not sure how I would prove this algebraically.

I would obviously have to prove that (x1)^T*x3 would ALWAYS have to equal 0 if it the statement was necessarily true... but I'm not sure how to go about doing that...

I'm completely stuck. I would greatly appreciate your help!
 
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  • #2
Try to think of an example.
 

FAQ: Transitive Property with Orthogonal Vectors?

1. What is the Transitive Property with Orthogonal Vectors?

The Transitive Property with Orthogonal Vectors is a mathematical property that states if two vectors are orthogonal to each other, and one of them is also orthogonal to a third vector, then the first vector is also orthogonal to the third vector.

2. How is the Transitive Property with Orthogonal Vectors used in scientific research?

The Transitive Property with Orthogonal Vectors is often used in scientific research to analyze and understand the relationships between different variables or elements. It allows scientists to make predictions and draw conclusions based on the properties of orthogonal vectors.

3. Can you provide an example of the Transitive Property with Orthogonal Vectors?

One example of the Transitive Property with Orthogonal Vectors is in the study of forces in physics. If two forces are acting on an object at right angles to each other, and one of the forces is also acting at right angles to a third force, then the first force is also acting at right angles to the third force.

4. What other properties does the Transitive Property with Orthogonal Vectors relate to?

The Transitive Property with Orthogonal Vectors is closely related to the Commutative Property, which states that the order of operations does not affect the outcome. It is also related to the Associative Property, which states that the grouping of operations does not affect the outcome.

5. Is the Transitive Property with Orthogonal Vectors applicable in all fields of science?

Yes, the Transitive Property with Orthogonal Vectors is a fundamental mathematical property that can be applied in all fields of science, from physics and engineering to biology and chemistry. It is a universal principle that helps us understand the relationships between different variables and elements in various scientific phenomena.

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