Vector Linear Combinations: Solving for Scalar Quantity

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Homework Help Overview

The discussion revolves around expressing vectors as linear combinations, specifically focusing on vectors directed at angles of 45 degrees and 150 degrees with given magnitudes. The subject area includes vector mathematics and linear algebra concepts.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find scalar quantities associated with the vectors but expresses difficulty in arriving at the correct answer. Some participants seek clarification on the basis of the linear combination, specifically the components involved (i and j).

Discussion Status

Participants are exploring different interpretations of the problem, with some providing hints and resources for further understanding. A hint regarding the use of direction cosines to find unit vectors has been offered, which appears to have helped the original poster progress in their understanding.

Contextual Notes

There is a mention of needing to clarify the components for the linear combination, which indicates potential assumptions or missing information regarding the setup of the problem.

Hollysmoke
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The question is to write the following vectors as a linear combination:

c) a vector directed at an angle of 45 degrees with a magnitude of square root of 2.

d)a vector directed at an angle of 150 degrees with a magnitude of 6.

What I tried to do is to find the scalar quantity with the vector but I'm not getting a right answer. Could someone please help me in the right direction?
 
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As a linear combination of what?
 
oh sorry. i+j
 
i and j. not i+j.
 
does anyone know any website that I could use as a tutorial, then?
 
Hint:First find a unit vector in the given direction using direction cosines.
Then multiply by magnitude.
 
Thank you for the websites and thank you for the help. I figured it out with that hint :D
 

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