anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
TuringTest
  • TuringTest
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\[\vec v\cdot(\vec u+\vec w)=\vec v\cdot\vec w+\vec v\cdot\vec u\]
anonymous
  • anonymous
yes. then? I got something not what i want. please, give me more
TuringTest
  • TuringTest
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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More answers

anonymous
  • anonymous
v.mu +v.kw
TuringTest
  • TuringTest
right, now how do the constants affect the dot product?
anonymous
  • anonymous
m+k
TuringTest
  • TuringTest
no, the scalars can be factored out of dot product multiplication\[\vec v\cdot(k\vec w)=k(\vec v\cdot\vec w)=?\]
anonymous
  • anonymous
kv.w
TuringTest
  • TuringTest
and what is \(\vec v\cdot\vec w\) ?
anonymous
  • anonymous
0
TuringTest
  • TuringTest
yes, so then what is\[\vec v\cdot(k\vec w)\]?
anonymous
  • anonymous
0
TuringTest
  • TuringTest
yes, so then what is\[\vec v\cdot(k\vec w+m\vec u)\]?
anonymous
  • anonymous
i got it now. my bad when make them = instead of adding together to get the answer, thanks a lot
TuringTest
  • TuringTest
you're welcome!
anonymous
  • anonymous
Let me put everything in neat, would you please check it for me?
anonymous
  • anonymous
how to put orthogonal symbol?
TuringTest
  • TuringTest
\perp
anonymous
  • anonymous
don't understand
ParthKohli
  • ParthKohli
\(\backslash ( \text{\perp}\backslash ) \)
TuringTest
  • TuringTest
are you trying to use the equation editor or are you writing in LaTeX ? ...yeah best is do what @ParthKohli wrote
ParthKohli
  • ParthKohli
``` \( v \perp u\) ```
anonymous
  • anonymous
\(\perp\) Lol. got it. thanks
anonymous
  • anonymous
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
anonymous
  • anonymous
by the way how to put vector symbol
TuringTest
  • TuringTest
\[\backslash(\text{\vec u}\backslash)\], and if you want to get good at writing equations try learning the language LaTeX
anonymous
  • anonymous
\(v\perp u\) ---> \(v\perp ku\) is it right?
anonymous
  • anonymous
what LateX means
anonymous
  • anonymous
\(v perp w\) ---> \(v perp mw\)
TuringTest
  • TuringTest
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
anonymous
  • anonymous
I will. thanks for all.
TuringTest
  • TuringTest
for what you are doing you should write\[\backslash [\text{\vec v \perp \vec w}\backslash ]\]backslashes and spaces are important
anonymous
  • anonymous
\[\vec v\perp\vec w\]. bingo
TuringTest
  • TuringTest
nice :) keep practicing LaTeX, it's handy!
anonymous
  • anonymous
I will. thank you very much.
anonymous
  • anonymous
\[\vec v\perp\vec w\]---> \[\vec v\perp\k vec w\]
anonymous
  • anonymous
ah .... mistake
TuringTest
  • TuringTest
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)
anonymous
  • anonymous
k\(\vec v\). bingo
TuringTest
  • TuringTest
very good :D\[\backslash[\text{\vec v\perp \vec w\iff \vec v\cdot\vec w=0}\backslash]\]gives\[\vec v\perp \vec w\iff \vec v\cdot\vec w=0\]
ParthKohli
  • ParthKohli
I never answered this question. A medal is definitely not needed here. Just doing my amby thing :-)
anonymous
  • anonymous
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.
TuringTest
  • TuringTest
@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.
ParthKohli
  • ParthKohli
@hoa It took me a lot of time too!
anonymous
  • anonymous
@ParthKohli . I don't know what you mean, but to me, being helpful person deserves all. I appreciate what others guide me.
anonymous
  • anonymous
@ParthKohli . the net automatically put the medal , i didn't do. or other put it there
ParthKohli
  • ParthKohli
Turing did. :-)
anonymous
  • anonymous
yes. my question is: what does the medal mean?
TuringTest
  • TuringTest
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.
anonymous
  • anonymous
why ? to me, it's just for showing the appreciateness
ParthKohli
  • ParthKohli
Mine wasn't too fair. :-P
TuringTest
  • TuringTest
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.
anonymous
  • anonymous
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
TuringTest
  • TuringTest
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.
anonymous
  • anonymous
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
TuringTest
  • TuringTest
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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