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

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The discussion focuses on troubleshooting parts (b), (c), and (e) of a problem related to the dot product. For part (b), participants are encouraged to write out the dot product formula and compare it with the right-hand side (RHS) to draw conclusions. In part (c), a similar approach is suggested, emphasizing the importance of analyzing the dot product formulas. Part (e) prompts a geometric interpretation, with advice to visualize examples to enhance understanding. The conversation highlights the need for clarity on geometric reasoning and the relationship between vectors and their negatives.
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 $-\mathbf{b}?$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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