## owlet one year ago Find a scalar equation of the plane that contains the point P(2,4,1) and is parallel to the plane $$2x_1 + 3x_2 -5x_3 = 6$$.

1. Loser66

just plug the numbers in.

2. owlet

|dw:1443664554238:dw| simplifying that, I got 11, so d =11 will the answer be 2x1 + 3x2 - 5x3 = 11?

3. owlet

that's what i did, just wanted to make sure if I'm right

4. owlet

i usually have a mistake in vector and scalar equations.. I usually switch them

5. owlet

can we fin vector equation from this?

6. Loser66

|dw:1443664955587:dw|

7. Loser66

|dw:1443665007633:dw|

8. owlet

ok thanks for confirming it :) can we find vector equation from this scalar equation? is it possible?

9. Loser66

why not? @chris00 now your turn

10. owlet

wait is there even a vector equation for a plane? O.o

11. anonymous

haha nice to throw the ball to me

12. Loser66

it's not hard, right? all of us know how to do, right?

13. anonymous

there is a normal vector equation for the plane...

14. anonymous

you can simply read that off

15. anonymous

what this represents is

16. anonymous

|dw:1443665293308:dw|

17. Loser66

hey, guy, give him the easiest way, please.

18. anonymous

isn't that just $(r-r _{o})n=0$ jeez, its been so long

19. owlet

got it, nvm

20. anonymous

where n is the normal?

21. anonymous

yolo

22. anonymous

what did ya do?

23. owlet

i am already doing another prob

24. anonymous

oh, sorry mate

25. anonymous

probs need a refresher since its been like 4yrs ago since I've done this lel

26. owlet

try this then: Verify the triangle inequality and the CAuchy-Schwarz inequality if: |dw:1443665710601:dw|

27. Loser66

2x1+3x2-5x3=11 $$x_1= 11/2 - (3/2)x_2 +(5/2)x_3$$ Hence vector equation is $$\vec x= \left[\begin{matrix}(11/2)-(3/2)x_2 +(5/2)x_3\\x_2\\x_3\end {matrix}\right]$$ Now, turn to $$\vec x= \left[\begin{matrix}11/2\\0\\0\end{matrix}\right]+ x_2\left[\begin{matrix}(-3/2)\\1\\0\end{matrix}\right]+x_3\left[\begin{matrix}(5/2)\\0\\1\end{matrix}\right]$$

28. Loser66

That is the easiest way to find the vector equation from a scalar one.

29. Loser66

just replace x2 = lambda 1 and x3 = lambda2

30. anonymous

$|u.v|\le|u||v|$

31. anonymous

i think thats the Cauchy schwartz inequality theorem

32. anonymous

pretty straight forward if u apply this, i rekn

33. owlet

ok got it..i use the other one: |dw:1443666019926:dw|

34. owlet

thanks.

35. anonymous

the triangle inequality?

36. anonymous
37. anonymous

u don't need to verify anything if u just proof it using variables

38. anonymous

cause a proof applies it for all cases. but its easier with numbers cause you just plug and chug it into formulas

39. owlet

it says on the question "Verify the Triangle Inequality"

40. anonymous

yea, probs best to just verify then. i was just giving you a proof for you to understand that it word for any case. perhaps you can read that in your own time to familiarise it for yourself

41. owlet

i will do that for sure :) I'm studying it right now. Thanks for all your help. Really appreciate it

42. anonymous

no problem. good luck :)