Finding a vector using scalar and vector projections

[user8899]

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?

 

[tiny-tim]

welcome to pf!

hi user8899! welcome to pf!

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?

 

[user8899]

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

 

[tiny-tim]

what is your vector projection equation?