## ranyai12 2 years ago Please Help! Parameterize the plane that contains the three points (3,−5,−2), (10,−12,−10), and (25,0,5). r(s,t)=

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1. ranyai12

I first assigned the points to P Q and R and then found PQ and PR and then put P+u<PQ>+v<PR> and I got <3+7s+22t,-5-7s+5t,-2-8s+7s> but got it wrong!

2. jim_thompson5910

what did you get for vector PQ

3. jim_thompson5910

4. ranyai12

I got <7,-7,-8>

5. ranyai12

Yes i looked at that and Im stll not sure what i dd wrong

6. jim_thompson5910

7. ranyai12

22,5,7

8. jim_thompson5910

ok, so far, so good

9. jim_thompson5910

I'm assuming you tried <3+7s+22t,-5-7s+5t,-2-8s+7t>and not <3+7s+22t,-5-7s+5t,-2-8s+7s> right?

10. ranyai12

i did it twice and got it wrong twice

11. jim_thompson5910

ok one sec

12. jim_thompson5910

does it specify at all which variables are the free variables (like x and y or x and z)?

13. ranyai12

no

14. jim_thompson5910

hmm well I managed to find a calculator that will give the equation of the plane

15. jim_thompson5910
16. jim_thompson5910

that equation is -x-25y+21z-80 = 0 -x-25y+21z= 80 solve for x: -x-25y+21z= 80 -x = 80+25y-21z x = -80-25y+21z

17. jim_thompson5910

so if you let y = s and z = t, then you will get <x, y, z> = <-80-25y+21z, y, z> <x, y, z> = <-80-25s+21t, s, t>

18. jim_thompson5910

unfortunately there are many ways to parameterize the plane

19. ranyai12

can you please provide me with an example

20. jim_thompson5910

what do you mean

21. ranyai12

as in please show me a way o parameterize this

22. jim_thompson5910

well you could take the cross product of vectors PQ and PR

23. jim_thompson5910

that will give you the normal vector to the plane

24. ranyai12

what would i do then

25. jim_thompson5910

what do you get when you do the cross product

26. ranyai12

gimme a sec

27. ranyai12

-89i+113j+189k

28. jim_thompson5910

somewhat close, but that's not correct

29. ranyai12

what is it then?

30. jim_thompson5910

try it again

31. ranyai12

ok