Question about vector coordinates

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Homework Help Overview

The discussion revolves around vector coordinates, specifically the relationship between points A, B, and C in a geometric context. Participants are exploring how to calculate vector segments and their relationships, particularly involving the origin and weighted averages.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of vector AB and its relation to finding vector AC. There is confusion regarding the correct multiplication factor and the involvement of the origin. Some suggest visual aids like drawings to clarify the problem. Others inquire about calculating weighted averages of vectors and their implications on the line segment.

Discussion Status

The discussion is active with various interpretations being explored. Some participants are questioning the original poster's calculations and assumptions, while others are providing guidance on concepts like weighted averages and vector representation. No consensus has been reached yet.

Contextual Notes

There is mention of potential confusion in the problem statement and the need for visual representation to aid understanding. Participants are also considering the implications of vector lengths and weights in their calculations.

homeworkhelpls
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Homework Statement
Find C position vector
Relevant Equations
none
1666203644182.png

here i found AB to be (-3, 2) and then i thought to do 2/5 multiplied by AB to find AC, however this is incorrect and instead i would have to involve the origin. Why and how can i involve the origin?
 
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The problem statement in combination with your attempt are confusing for me. Can you upload a drawing of this line please? Thanks.
 
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homeworkhelpls said:
here i found AB to be (-3, 2) and then i thought to do 5/2 multiplied by AB to find AC
I think AB here is supposed to be the length of the line segment connecting points A and B. It's not the vector ##\mathbf{b}-\mathbf{a}##, though it is related. And I think you meant you multiplied by 2/5, not 5/2. Or at least that would somewhat make sense.

Anyways, draw a sketch. I think it'll help you understand what the problem is asking for.
 
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Do you know how to calculate a weighted average of vectors ##a## and ##b## so that ##a## gets 3/5 of the weight and ##b## gets 2/5? Would that point be on the AB line? How do the lengths of the AC and CB relate to the weights of the average?
 
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Consider \mathbf{x}(t) = (1-t)\mathbf{a} + t\mathbf{b} for 0 \leq t \leq 1
 
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