Infinite number of perpendicular vectors?

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SUMMARY

The discussion centers on the construction of unit vectors in three-dimensional space, specifically focusing on vectors A = (2,-1,3) and B = (1,4,1). Participants confirm the completion of tasks to find unit vectors A' and B' parallel to A and B, and to construct all unit vectors C orthogonal to A' and B'. The main query is whether there exists an infinite number of vectors D such that the dot product C.D equals zero, which is affirmed as true, although the task only requires finding one such vector D.

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  • Understanding of vector operations, including dot products and orthogonality.
  • Familiarity with unit vectors and their properties.
  • Knowledge of three-dimensional Cartesian coordinates.
  • Basic skills in linear algebra concepts.
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  • Study the properties of orthogonal vectors in three-dimensional space.
  • Learn about the geometric interpretation of dot products.
  • Explore methods for constructing unit vectors from given vectors.
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Students studying linear algebra, educators teaching vector mathematics, and anyone interested in the geometric properties of vectors in three-dimensional space.

Maybe_Memorie
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Homework Statement


Let A and B be vectors
A = (2,-1,3) B = (1,4,1)
a) Find unit vectors A' and B' parallel to A and B respectively. Done.

b) Construct all the unit vectors C, orthogonal to A' and B'. Done.

c) Construct a unit vector, D, such that
C.D = 0.


Isn't there an infinite number of vectors that meet this criteria?
 
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Maybe_Memorie said:
b) Construct all the unit vectors C, orthogonal to A' and B'. Done.

c) Construct a unit vector, D, such that
C.D = 0.


Isn't there an infinite number of vectors that meet this criteria?

Well I think they just want you to find one, which you can do since you did part b already.
 

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