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

[Monoxdifly]

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:
\(\displaystyle \cos\theta=\frac{u\cdot w}{|u||w|}\) and \(\displaystyle \cos\phi=\frac{v\cdot w}{|v||w|}\)
Then I substituted them as |v| and |u| to the given equation and got:
\(\displaystyle w=\frac{v\cdot w}{|w|\cos\phi}\cdot u+\frac{u\cdot w}{|w|\cos\theta}\cdot v\)
What to do after this? I am stuck.

 

[Evgeny.Makarov]

I would use the fact that \(\displaystyle \lvert\lvert u\rvert\cdot v\rvert=\lvert\lvert v\rvert \cdot u\rvert\) and look at the sum geometrically.

 

[PeterOwen]

I look at your post and don't understant a thing. Can you explain everything to me?

 

[Evgeny.Makarov]

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 \(\displaystyle \lvert v\rvert\) 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?"