Troubleshooting (b), (c) & (e): Seeking Assistance

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Discussion Overview

The discussion revolves around troubleshooting specific parts of a problem set, particularly parts (b), (c), and (e), which involve the dot product and geometric interpretations. The focus is on seeking assistance and clarification regarding these concepts.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in answering parts (b), (c), and (e) of the problem set and requests help.
  • Another participant suggests writing out the formula for the dot product and comparing it with the right-hand side (RHS) to draw conclusions for parts (b) and (c).
  • For part (e), a geometric approach is recommended, including drawing examples to aid understanding.
  • A later reply seeks clarification on the geometric interpretation suggested for part (e) and requests further advice.
  • Another hint is provided regarding the relationship between vectors, specifically comparing $\mathbf{a}+\mathbf{b}$ with $\mathbf{a}+(-\mathbf{b})$ to gain insights into the problem.

Areas of Agreement / Disagreement

Participants are engaged in a collaborative troubleshooting effort, with no consensus reached yet on the specific interpretations or solutions for parts (b), (c), and (e).

Contextual Notes

There are unresolved aspects regarding the geometric interpretation in part (e) and the specific conclusions that can be drawn from the dot product comparisons in parts (b) and (c).

Joe20
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I have some difficulties answering part (b), (c) and (e).

Help is appreciated.
 

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(b) If you write out the formula for the dot product, what do you get? Now compare that with the RHS. What can you conclude?

(c) Again, I would write out the formulae for the dot products. What can you conclude?

(e) I would think about this one geometrically. Try drawing a few examples and see what you come up with.
 
Ackbach said:
(b) If you write out the formula for the dot product, what do you get? Now compare that with the RHS. What can you conclude?

(c) Again, I would write out the formulae for the dot products. What can you conclude?

(e) I would think about this one geometrically. Try drawing a few examples and see what you come up with.
Hi Ackbach,

Thanks for the advice. I am not very sure what is meant by thinking it geometrically and drawing a few examples in part (e). Would further advice on this. Thanks.
 
Alexis87 said:
Hi Ackbach,

Thanks for the advice. I am not very sure what is meant by thinking it geometrically and drawing a few examples in part (e). Would further advice on this. Thanks.

Well, here's another hint: $\mathbf{a}-\mathbf{b}=\mathbf{a}+(-\mathbf{b})$. So, comparing $\mathbf{a}+\mathbf{b}$ with $\mathbf{a}+(-\mathbf{b})$ gives you some information about what's going on. Geometrically, how does $\mathbf{b}$ compare with $-\mathbf{b}?$
 

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