Finding a vector using scalar and vector projections

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Homework Help Overview

The problem involves finding a vector based on its vector projection onto a given vector and its scalar projection onto another vector. The subject area pertains to vector projections in linear algebra.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the initial setup involving the vector projection equation and the scalar projection. There is an attempt to express the unknown vector in terms of its components, and questions arise regarding the relationship between scalar and vector projections.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning the algebraic steps involved. Some guidance has been offered regarding the nature of scalar projections, but no consensus has been reached on the next steps.

Contextual Notes

Participants are navigating potential algebraic difficulties and clarifying definitions related to vector projections. There may be assumptions about the relationships between the projections that are being examined.

user8899
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Homework Statement



Determine the vector(s) whose vector projection on u =< 1,2,2 > is v =< 3,6,6 > and its
scalar projection on w =< 1,1,1 > is √3.

Homework Equations


Vector Projection of b onto a: (|b.a| \ |a|) * (1/ |a|) * a
Scalar Projection: (|b.a| \ |a|)


The Attempt at a Solution


First started by finding the vector <a,b,3-b-c> (using the scalar projection equation), but don't know what else to do from there. Help please?
 
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welcome to pf!

hi user8899! welcome to pf! :smile:
user8899 said:
First started by finding the vector <a,b,3-b-c> (using the scalar projection equation) …

isn't the scalar projection just the magnitude of the vector projection? :wink:
 
Hi, Thank you!

well I substituted <a,b,3-b-c> into the vector projection equation, but I think my problem is the algebra... I'm not sure
 
what is your vector projection equation? :smile:
 

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