Drawing Geometry Questions: Can You Help?

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    Drawing Geometry
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Discussion Overview

The discussion revolves around the correctness of drawn geometric representations related to vector operations, specifically focusing on the application of the parallelogram law and vector addition/subtraction. Participants seek clarification on their drawings and the methodology for representing vectors accurately.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks for confirmation on the accuracy of their drawings and expresses difficulty with part (f).
  • Another participant questions whether the direction of vector b should be reversed in their drawing.
  • A participant explains two methods for understanding vector subtraction, emphasizing the tip-to-tail method and the tail-to-tail method.
  • Some participants agree that vector b should be represented in the opposite direction as -b, confirming the correctness of the drawing.
  • One participant suggests that part (f) can be approached by flipping vector a to -a and connecting it to the tail of 2b, which is drawn twice in length.
  • A later reply emphasizes the need to specify which part of -a is connected to 2b, indicating a potential point of confusion.
  • Another participant expresses satisfaction with the drawings, indicating they appear correct.

Areas of Agreement / Disagreement

Participants generally agree on the methods for drawing the vectors and the correctness of certain representations, but there are points of clarification needed regarding the connections of vectors, particularly in part (f). Multiple views on the representation of vector directions remain present.

Contextual Notes

Some assumptions about vector directionality and connection points are not explicitly stated, which may lead to varying interpretations of the drawings.

ineedhelpnow
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can someone tell me if i drew these right. and also I am stuck on part (f). how do i draw that? i attached the original questions and my drawings.

View attachment 2955

View attachment 2954

for part (a) and (e) i used the parallelogram law
 

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for (b) should my b vector be pointing the other direction?
 
6a to e is right. B is right, but if you want to know, there's two ways to think about it:

b) $a-b = a+-b$

We can apply what we know about adding vectors tip to tail. That is the easiest way to think about it, and I think most people use that way. However, you can also apply vector subtraction, such as $a-b$, by connecting the vectors tail to tail. The resultant vector's tail will be on the tip of $a$, and point towards (the tip of) $b$. (that is easy to prove). So for B, your resultant vector indeed points from $b$ to $a$, which is correct.
 
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yes that's how i see it. a+(-b) so should my b in that drawing be point in the opposite direction (-b)?
 
ineedhelpnow said:
yes that's how i see it. a+(-b) so should my b in that drawing be point in the opposite direction (-b)?

It's correct as it is. Although, you can physically redraw the vector $b$ as $-b$ by flipping the vector, and connect it head to tail with vector A. This should produce the same vector as you have drawn above. Alternative, you can draw the whole parallelogram, as the following:
http://upload.wikimedia.org/wikiped...llelogram_law.PNG/220px-Parallelogram_law.PNG

- - - Updated - - -

f) is based on the same principle.
$$2b-a$$
We can rewrite it as $2b+ (-a)$. Now we can draw $b$ twice its length, and flip the vector $a$ in the opposite direction. Now connect them head to tail to draw the resultant vector.
 
for part (f) i flipped vector a so now its -a and its connected to the tail of 2b (b twice in length) and for (b) i flipped the vector in the opposite direction so it is now -b and is connected to the tail of a. correct?
 
Although I think you are right, you have to specify which part of $-a$ (head or tail) that is connected to the tail of $2b$.
 

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Those look correct. :D
 
  • #10
Thanks Rido!
 

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