MHB Skype is a communication software and a notebook is a small portable computer.

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The discussion revolves around a mathematical problem involving vectors and angles, specifically focusing on the relationships between angles θ and φ derived from the equation w = |v|∙u + |u|∙v. Participants express confusion over the geometric interpretation and mathematical proofs related to the angles and vector products. One user seeks clarification on the formula involving the lengths of vectors, indicating a lack of understanding of its implications. The conversation also humorously contrasts the technical discussion with a basic inquiry about Skype and notebooks, highlighting the importance of clear communication in both contexts. Overall, the thread emphasizes the need for clearer explanations in mathematical discussions.
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Given w = |v|∙ u + |u| ∙ v. If θ = ∠(u ∙ w) and φ = ∠(v ∙ w) then ….
a. Φ – θ = 90°
b. θ + φ= 90°
c. θ = φ
d. θ – φ = 90°
e. θ – φ = 180°

What I have done:
$$\cos\theta=\frac{u\cdot w}{|u||w|}$$ and $$\cos\phi=\frac{v\cdot w}{|v||w|}$$
Then I substituted them as |v| and |u| to the given equation and got:
$$w=\frac{v\cdot w}{|w|\cos\phi}\cdot u+\frac{u\cdot w}{|w|\cos\theta}\cdot v$$
What to do after this? I am stuck.
 
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I would use the fact that $$\lvert\lvert u\rvert\cdot v\rvert=\lvert\lvert v\rvert \cdot u\rvert$$ and look at the sum geometrically.
 
I look at your post and don't understant a thing. Can you explain everything to me?
 
PeterOwen said:
I look at your post and don't understant a thing.
Sorry, I am not convinced. I am using the notations you also used in the problem statement, namely, the length $$\lvert v\rvert$$ of a vector $v$ and the product $x\cdot v$ of a number $x$ and a vector $v$. How can you say you don't understand the formula $\lvert\lvert u\rvert\cdot v\rvert=\lvert\lvert v\rvert \cdot u\rvert$? Perhaps its proof may not be obvious, though it is, but its meaning should be clear. Otherwise we have a dialog like the following.

"Could you help me start Skype on my notebook?"
"Just look at the bottom of your notebook's screen and click the Skype icon."
"What is Skype and what is a notebook?"
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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