Finding a vector using scalar and vector projections

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The discussion revolves around finding a vector that meets specific projection criteria. The vector projection of a vector u onto another vector v is given, and the scalar projection onto a third vector w is also specified. Participants are attempting to derive the vector using algebraic methods but are encountering difficulties with the calculations. Clarifications about the relationships between vector and scalar projections are discussed, particularly the connection between their magnitudes. The conversation highlights the challenges in applying the correct equations to solve the problem effectively.
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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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