Proving Vector Orthogonality of b onto a

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SUMMARY

The discussion focuses on proving that the vector orthogonal to vector b onto vector a, defined as b minus the projection of b onto a, is orthogonal to vector a. The key concepts involved include the definition of vector projection and the geometric interpretation of the dot product. Understanding these concepts is essential for solving the problem effectively. Participants emphasize the importance of reviewing lecture notes or textbooks for clarity on these definitions.

PREREQUISITES
  • Vector projection concepts
  • Geometric interpretation of the dot product
  • Basic linear algebra principles
  • Understanding of orthogonal vectors
NEXT STEPS
  • Review vector projection formulas and properties
  • Study the geometric interpretation of the dot product
  • Explore the concept of orthogonal vectors in linear algebra
  • Practice problems involving vector projections and orthogonality
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Students studying linear algebra, particularly those tackling vector projections and orthogonality, as well as educators looking for teaching resources on these topics.

darthxepher
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Homework Statement



Show that vector orth of b onto a=b-proj of b onto a is orthogonal to a.


I totally don't know where to start :(

and I don't know hat orth of b onto a means...
 
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darthxepher said:
and I don't know hat orth of b onto a means...

Well, that's kind of crucial for answering this question, isn't it. Do you have any lecture notes or textbook in which you can look this up?
Do you remember what the dot product ([itex]\vec a \cdot \vec b[/itex]) meant geometrically?
 

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