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

- anonymous

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- 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

yes. then? I got something not what i want. please, give me more

- 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

v.mu +v.kw

- TuringTest

right, now how do the constants affect the dot product?

- anonymous

m+k

- 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

kv.w

- TuringTest

and what is \(\vec v\cdot\vec w\) ?

- anonymous

0

- TuringTest

yes, so then what is\[\vec v\cdot(k\vec w)\]?

- anonymous

0

- TuringTest

yes, so then what is\[\vec v\cdot(k\vec w+m\vec u)\]?

- anonymous

i got it now. my bad when make them = instead of adding together to get the answer, thanks a lot

- TuringTest

you're welcome!

- anonymous

Let me put everything in neat, would you please check it for me?

- anonymous

how to put orthogonal symbol?

- TuringTest

\perp

- anonymous

don't understand

- ParthKohli

\(\backslash ( \text{\perp}\backslash ) \)

- TuringTest

are you trying to use the equation editor or are you writing in LaTeX ?
...yeah best is do what @ParthKohli wrote

- ParthKohli

```
\( v \perp u\)
```

- anonymous

\(\perp\)
Lol. got it. thanks

- 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

by the way how to put vector symbol

- TuringTest

\[\backslash(\text{\vec u}\backslash)\], and if you want to get good at writing equations try learning the language LaTeX

- anonymous

\(v\perp u\) ---> \(v\perp ku\) is it right?

- anonymous

what LateX means

- anonymous

\(v perp w\) ---> \(v perp mw\)

- 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

I will. thanks for all.

- TuringTest

for what you are doing you should write\[\backslash [\text{\vec v \perp \vec w}\backslash ]\]backslashes and spaces are important

- anonymous

\[\vec v\perp\vec w\]. bingo

- TuringTest

nice :)
keep practicing LaTeX, it's handy!

- anonymous

I will. thank you very much.

- anonymous

\[\vec v\perp\vec w\]---> \[\vec v\perp\k vec w\]

- anonymous

ah .... mistake

- 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

k\(\vec v\). bingo

- 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

I never answered this question. A medal is definitely not needed here. Just doing my amby thing :-)

- 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

@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

@hoa It took me a lot of time too!

- anonymous

@ParthKohli . I don't know what you mean, but to me, being helpful person deserves all. I appreciate what others guide me.

- anonymous

@ParthKohli . the net automatically put the medal , i didn't do. or other put it there

- ParthKohli

Turing did. :-)

- anonymous

yes. my question is: what does the medal mean?

- 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

why ? to me, it's just for showing the appreciateness

- ParthKohli

Mine wasn't too fair. :-P

- 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

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

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

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

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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