Finding Parallel and Orthogonal Vectors for u and v

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Homework Help Overview

The problem involves finding two vectors, u1 and u2, based on the given vectors u and v. Specifically, u1 should be parallel to v, while u2 should be orthogonal to v, with the condition that u equals the sum of u1 and u2. The subject area pertains to vector mathematics, particularly concepts of parallelism and orthogonality.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to begin solving the problem and seek clarification on the definitions of parallel and orthogonal vectors. Some suggest that drawing a diagram could be beneficial, while others question the absence of relevant equations in the original post.

Discussion Status

The discussion is ongoing, with participants exploring different aspects of the problem. There is a focus on understanding the definitions and properties of parallel and orthogonal vectors, but no consensus has been reached on a specific approach or solution.

Contextual Notes

One participant notes that their textbook does not mention parallel vectors, which raises questions about the assumptions underlying the problem. Additionally, there is a mention of the dot product being relevant for determining orthogonality.

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Homework Statement



For u=(26, 6, 21) and v=(−27, −9, −18) , find the vectors u1 and u2 such that:

(i) u1 is parallel to v

(ii) u2 is orthogonal to v

(iii) u = u1 + u2


Homework Equations



None

The Attempt at a Solution



I'm quite lost on this question and not sure how to even start. Can someone explain the question and give me some hints to get started?

Thanks in advance.
 
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Are you sure that there are no relevant equations? What about those defining defining parallel and orthogonal?
 
Drawing a diagram is always great.
 
There aren't any other questions or equations about this. All I know is if their dot product is 0, then its orthogonal, and my book doesn't even mention parallel.
 

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