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

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SUMMARY

This discussion focuses on troubleshooting parts (b), (c), and (e) of a mathematical problem involving dot products and geometric interpretations. Participants emphasize the importance of writing out the formulas for dot products to draw conclusions about the relationships between vectors. Additionally, they suggest visualizing the problem geometrically to enhance understanding, particularly in part (e), where comparing vectors and their negatives is crucial. The advice provided includes hints for deeper analysis and geometric reasoning.

PREREQUISITES
  • Understanding of vector mathematics and dot products
  • Familiarity with geometric interpretations of vectors
  • Basic knowledge of algebraic manipulation of vector equations
  • Ability to visualize mathematical concepts through diagrams
NEXT STEPS
  • Study the properties of dot products in vector algebra
  • Explore geometric interpretations of vector addition and subtraction
  • Learn how to visualize vector relationships using diagrams
  • Investigate the implications of vector negation in geometric contexts
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Students and educators in mathematics, particularly those focusing on vector analysis and geometric interpretations of algebraic concepts.

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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