Question

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

Answer 1

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\[\vec v\cdot(\vec u+\vec w)=\vec v\cdot\vec w+\vec v\cdot\vec u\]

Answer 2

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

Answer 3

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?

Answer 4

v.mu +v.kw

Answer 5

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

Answer 6

m+k

Answer 7

no, the scalars can be factored out of dot product multiplication\[\vec v\cdot(k\vec w)=k(\vec v\cdot\vec w)=?\]

Answer 8

kv.w

Answer 9

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

Answer 10

0

Answer 11

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

Answer 12

0

Answer 13

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

Answer 14

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

Answer 15

you're welcome!

Answer 16

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

Answer 17

how to put orthogonal symbol?

Answer 18

\perp

Answer 19

don't understand

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

by the way how to put vector symbol

Answer 26

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

Answer 27

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

Answer 28

what LateX means

Answer 29

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

Answer 30

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

Answer 31

I will. thanks for all.

Answer 32

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

Answer 33

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

Answer 34

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

Answer 35

I will. thank you very much.

Answer 36

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

Answer 37

ah .... mistake

Answer 38

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)

Answer 39

k\(\vec v\). bingo

Answer 40

very good :D\[\backslash[\text{\vec v\perp \vec w\iff \vec v\cdot\vec w=0}\backslash]\]gives\[\vec v\perp \vec w\iff \vec v\cdot\vec w=0\]

Answer 41

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

Answer 42

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.

Answer 43

@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.

Answer 44

@hoa It took me a lot of time too!

Answer 45

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

Answer 46

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

Answer 47

Turing did. :-)

Answer 48

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

Answer 49

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.

Answer 50

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

Answer 51

Mine wasn't too fair. :-P

Answer 52

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.

Answer 53

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

Answer 54

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.

Answer 55

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

Answer 56

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!