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show that if vector v is orthogonal with vector w and u, then v orthogonal with (kw + mu) for all k and m. Please help

Mathematics
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If two vectors are orthogonal, then their dot product is zero\[\vec v\perp\vec w\implies\vec v\cdot\vec w=0\]now remember that constants can be factored our of the dot product\[\vec v\cdot(k\vec w)=k(\vec v\cdot\vec w)\]and that the dot product is distributive\[\vec v\cdot(\vec u+\vec w)=\vec v\cdot\vec w+\vec v\cdot\vec u\]
yes. then? I got something not what i want. please, give me more
I'm not going to do the whole problem, I am just here to guide you. Take the dot product following what I have written above to evaluate\[\vec v\cdot(k\vec w+m\vec u)\]What do you get?

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Other answers:

v.mu +v.kw
right, now how do the constants affect the dot product?
m+k
no, the scalars can be factored out of dot product multiplication\[\vec v\cdot(k\vec w)=k(\vec v\cdot\vec w)=?\]
kv.w
and what is \(\vec v\cdot\vec w\) ?
0
yes, so then what is\[\vec v\cdot(k\vec w)\]?
0
yes, so then what is\[\vec v\cdot(k\vec w+m\vec u)\]?
i got it now. my bad when make them = instead of adding together to get the answer, thanks a lot
you're welcome!
Let me put everything in neat, would you please check it for me?
how to put orthogonal symbol?
\perp
don't understand
\(\backslash ( \text{\perp}\backslash ) \)
are you trying to use the equation editor or are you writing in LaTeX ? ...yeah best is do what @ParthKohli wrote
``` \( v \perp u\) ```
\(\perp\) Lol. got it. thanks
i need time to practice how to use the symbol. do many time but delete all at the end, sorry , waste your time, I try and send you mine in perfect . thanks thanks a lot for help in material
by the way how to put vector symbol
\[\backslash(\text{\vec u}\backslash)\], and if you want to get good at writing equations try learning the language LaTeX
\(v\perp u\) ---> \(v\perp ku\) is it right?
what LateX means
\(v perp w\) ---> \(v perp mw\)
LaTeX is the language used to write the math symbols. enclose things in brackets like so: \[ code \.] or \( code \.) (do not put the period, I just did that to illustrate how to put the backslashes and brackets http://omega.albany.edu:8008/Symbols.html yes
I will. thanks for all.
for what you are doing you should write\[\backslash [\text{\vec v \perp \vec w}\backslash ]\]backslashes and spaces are important
\[\vec v\perp\vec w\]. bingo
nice :) keep practicing LaTeX, it's handy!
I will. thank you very much.
\[\vec v\perp\vec w\]---> \[\vec v\perp\k vec w\]
ah .... mistake
You are welcome! another tip: if you want to know how somebody wrote something, hover your cursor over the latex you want to know the code for and press right click -> show math as -> Tex commands and you can see the source code and copy and paste it into\[\backslash[\dots\backslash]\text{ or }\backslash(\dots\backslash)\] It takes some practice to avoid syntax errors. The arrow can be done with \implies, though i? I think a double arrow is better here \iff (if and only if)
k\(\vec v\). bingo
very good :D\[\backslash[\text{\vec v\perp \vec w\iff \vec v\cdot\vec w=0}\backslash]\]gives\[\vec v\perp \vec w\iff \vec v\cdot\vec w=0\]
I never answered this question. A medal is definitely not needed here. Just doing my amby thing :-)
i am using other's computer, and i don't know how to copy the conversation to read later or follow when practice. so i have to copy by hand what you guide. it takes time.
@parth But I never thought to show latex by writing \backslash the way you did, and that proved very useful :) @hoa typing in latex does take some time, but of course it becomes less when you get used to it.
@hoa It took me a lot of time too!
@ParthKohli . I don't know what you mean, but to me, being helpful person deserves all. I appreciate what others guide me.
@ParthKohli . the net automatically put the medal , i didn't do. or other put it there
Turing did. :-)
yes. my question is: what does the medal mean?
Giving medals for best answer raises the recipients SmartScore. Parth and I have already gotten our fair share, that's why we're level 99.
why ? to me, it's just for showing the appreciateness
Mine wasn't too fair. :-P
I don't think most high-level users care much about scores and medals. It's just a sort of acknowledgement, but the teaching is what really matters.
ok. I got it. I make question "iff" need explanation, so whenever there is someone helps me, i give medal to show my appreciation no matter what it 's the best answer or not . now, i know what it means, thanks
No, you should really only give a medal if you think the user really *deserves* it. Feel free not to give one for those who only try to give answers without teaching, of which there are many.
they know who they are no matter how many medals they have, right? we are self- respect, they are the same. However, if you say so, I will be careful in giving medal. And if you say so, I feel my medal does not deserve at all. All my answer is for very very easy problems. shame on me
Don't feel bad, just help people in a way you can be proud of. Try to teach others, regardless of the level of the question and you will do great here!

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