Find Projection of (A+C) in B's Direction

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Homework Help Overview

The problem involves vector operations, specifically the projection of the sum of two vectors (A and C) in the direction of another vector (B). The vectors are defined in three-dimensional space.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the projection of (A + C) onto B and has calculated the sum of A and C. They also consider using the dot product and the unit vector of B. Some participants confirm the relevance of the dot product and question whether the angle between the vectors is being sought.

Discussion Status

Participants are clarifying the nature of the question, distinguishing between finding an angle and determining the projection of one vector onto another. There is a productive exchange regarding the correct interpretation of the problem.

Contextual Notes

Participants are navigating the definitions and relationships between vectors, particularly in the context of projections and angles, without reaching a definitive conclusion on the method to be used.

LocalStudent
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Homework Statement



The following are all vectors:
A = <2, 1, 1>
B = <1, -2, 2>
C = <3, -4, 2>

Find the projection of (A + C) in the direction of B

Homework Equations



Dot product?


The Attempt at a Solution



I was not sure what the meant in this question.

I added A and C and I got (A+C) = <5, -3, 3>

Then I did (A+C)dot(B) and I got that equal to 16



I was also thinking of dotting (A+C) with the unit vector of B?
 
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Dot product is exactly what you want to do. :smile:

[tex]\vec{X}\cdot\vec{Y} = |X|\cdot|Y|cos\theta[/tex]

You have the dot product, |X|, |Y|, and you need cosine of the angle :wink:
 
Infinitum said:
Dot product is exactly what you want to do. :smile:

[tex]\vec{X}\cdot\vec{Y} = |X|\cdot|Y|cos\theta[/tex]

You have the dot product, |X|, |Y|, and you need cosine of the angle :wink:


So is the question basically asking "What is the angle between (A+C) and B?"
 
LocalStudent said:
So is the question basically asking "What is the angle between (A+C) and B?"

No, it is asking you for the projection(component) of A+C on B. What is the component of a vector X on another vector Y when the angle between them is θ??
 
Infinitum said:
No, it is asking you for the projection(component) of A+C on B. What is the component of a vector X on another vector Y when the angle between them is θ??

ok, I see. Thanks for the help.
 

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