Vectors Parallel and Perpendicular

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Homework Help Overview

The discussion revolves around the representation of vector w in terms of components parallel and perpendicular to vector v, specifically using the equation w = g + h, where g is parallel to v and h is perpendicular to v. The subject area involves vector analysis and properties of dot products.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to start the problem, particularly regarding the decomposition of vector w into components g and h. Questions are raised about the general forms of vectors that are parallel and perpendicular to v.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the definitions and forms of parallel and perpendicular vectors. Some guidance has been offered in the form of questions aimed at understanding these concepts better, but no consensus or clear direction has emerged yet.

Contextual Notes

Participants indicate confusion regarding the specific requirements of the problem, particularly the notation w = g + h, and express a need for examples or definitions of perpendicular vectors in relation to vector v.

chodge17
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Homework Statement




Let vector v=<1,-2, 6> and vector w=<30,-11, -2>. Represent vector w in the form of

w=g+h, where g is parallel to v and h is perpendicular to v. Using the dot product


Homework Equations





The Attempt at a Solution


I don't even know where to begin. I think you maybe do v*w first but I don't know.
 
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Do you know the general form of vectors parallel to v? Do you know the general form of vectors perpendicular to v?
 
In most cases, yes. But in this instant, I don't know where to begin. What throws me off is the w=g+h. I know what the question is asking I just don't know how it is asking it. The question is wanting me to find vector g< , , , > and vector h< , , , >
 
Can you give me a vector perpendicular to v?
 

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