## Hoa Group Title 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 one year ago one year ago

1. TuringTest Group Title

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$\vec v\cdot(\vec u+\vec w)=\vec v\cdot\vec w+\vec v\cdot\vec u$

2. Hoa Group Title

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

3. TuringTest Group Title

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?

4. Hoa Group Title

v.mu +v.kw

5. TuringTest Group Title

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

6. Hoa Group Title

m+k

7. TuringTest Group Title

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

8. Hoa Group Title

kv.w

9. TuringTest Group Title

and what is $$\vec v\cdot\vec w$$ ?

10. Hoa Group Title

0

11. TuringTest Group Title

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

12. Hoa Group Title

0

13. TuringTest Group Title

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

14. Hoa Group Title

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

15. TuringTest Group Title

you're welcome!

16. Hoa Group Title

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

17. Hoa Group Title

how to put orthogonal symbol?

18. TuringTest Group Title

\perp

19. Hoa Group Title

don't understand

20. ParthKohli Group Title

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

21. TuringTest Group Title

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

22. ParthKohli Group Title

 $$v \perp u$$ 

23. Hoa Group Title

$$\perp$$ Lol. got it. thanks

24. Hoa Group Title

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

25. Hoa Group Title

by the way how to put vector symbol

26. TuringTest Group Title

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

27. Hoa Group Title

$$v\perp u$$ ---> $$v\perp ku$$ is it right?

28. Hoa Group Title

what LateX means

29. Hoa Group Title

$$v perp w$$ ---> $$v perp mw$$

30. TuringTest Group Title

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 31. Hoa Group Title I will. thanks for all. 32. TuringTest Group Title for what you are doing you should write\[\backslash [\text{\vec v \perp \vec w}\backslash ]$backslashes and spaces are important 33. Hoa Group Title $\vec v\perp\vec w$. bingo 34. TuringTest Group Title nice :) keep practicing LaTeX, it's handy! 35. Hoa Group Title I will. thank you very much. 36. Hoa Group Title $\vec v\perp\vec w$---> $\vec v\perp\k vec w$ 37. Hoa Group Title ah .... mistake 38. TuringTest Group Title 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) 39. Hoa Group Title k\(\vec v$$. bingo

40. TuringTest Group Title

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

41. ParthKohli Group Title

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

42. Hoa Group Title

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.

43. TuringTest Group Title

@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.

44. ParthKohli Group Title

@hoa It took me a lot of time too!

45. Hoa Group Title

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

46. Hoa Group Title

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

47. ParthKohli Group Title

Turing did. :-)

48. Hoa Group Title

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

49. TuringTest Group Title

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.

50. Hoa Group Title

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

51. ParthKohli Group Title

Mine wasn't too fair. :-P

52. TuringTest Group Title

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.

53. Hoa Group Title

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

54. TuringTest Group Title

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.

55. Hoa Group Title

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

56. TuringTest Group Title

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!