Expressing A Vector Given Another Vectors

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Homework Help Overview

The problem involves expressing a vector in terms of other vectors within the context of a square, specifically relating to points located at the midpoints of its sides. The original poster presents a multiple-choice question regarding the expression for vector AQ based on vectors a and b, which represent segments of the square.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the representation of vectors in terms of other vectors, suggesting a need to express all segments in consistent terms. There is mention of using a diagram to aid understanding, and some participants express confusion about the reasoning behind the multiple-choice answers.

Discussion Status

The discussion is ongoing, with participants providing hints and suggestions for approaching the problem. There is an emphasis on exploring the relationships between the vectors and the geometry of the square, but no consensus or resolution has been reached yet.

Contextual Notes

Some participants question the naming conventions of the vectors and the assumptions made about the problem setup. There is also a reference to the problem being part of a competition, which may impose additional constraints on the approach taken.

wiraimperia
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Homework Statement


ABCD is a square (AB = AD = BC = CD). The point P and Q are located in the middle of BC and CD. If AP and AD is expressed by the name vector a and b, then AQ = ...
A) (1/2)a + (3/4)b
B) (1/3)a + (2/3)b
C) (3/4)a + (1/2)b
D) (2/3)a + (1/3)b
E) (2/3)a + (3/4)b


Homework Equations


Vector addition law (still confused)


The Attempt at a Solution


This problem comes in a competition about 4 months ago. I just chose the answer A (random guessing) and thank God the answer is A. But how do we find it?
 
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welcome to pf!

hi wiraimperia! welcome to pf! :smile:

for some reason, AD is called "b" :rolleyes:

so let's call AB "d" :biggrin:

then express everything in terms of b and d …

what do you get? :smile:
 
A picture always helps.

ehild
 

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:-p
 


tiny-tim said:
hi wiraimperia! welcome to pf! :smile:

for some reason, AD is called "b" :rolleyes:

so let's call AB "d" :biggrin:

then express everything in terms of b and d …

what do you get? :smile:

We refer to the multiple choice answers... Not a made-up answer... And I'm still confused why it is (1/2)a + (3/4)b :confused:
 
Pretend that it is a "made-up" problem and find the vector AQ in terms of a and b. Follow tiny-tim's hint.

ehild
 
Remember a vector can be represented by a segment of a line
You can put anywhere the line/vector with the same direction/parallel.
 
Just draw two lines through Q, one parallel to b and the other parallel to a. These lines will cut b and a to the appropriate lengths and these lenghts can be determined by using the similarity triangles in the case of a and the 30-60 triangle in the case of b.
 
Last edited:

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