Question

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

Answer 1

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!

Answer 2

what did you get for vector PQ

Answer 3

btw, this page may help you out

http://math.harvard.edu/~ytzeng/worksheet/0926_sol.pdf

see page 3

Answer 4

I got <7,-7,-8>

Answer 5

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

Answer 6

how about PR?

Answer 7

22,5,7

Answer 8

ok, so far, so good

Answer 9

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?

Answer 10

i did it twice and got it wrong twice

Answer 11

ok one sec

Answer 12

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

Answer 13

no

Answer 14

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

Answer 15

http://www.wolframalpha.com/input/?i=plane+through+points+%283%2C%E2%88%925%2C%E2%88%922%29%2C+%2810%2C%E2%88%9212%2C%E2%88%9210%29%2C+and+%2825%2C0%2C5%29

Answer 16

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

Answer 17

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>

Answer 18

unfortunately there are many ways to parameterize the plane

Answer 19

can you please provide me with an example

Answer 20

what do you mean

Answer 21

as in please show me a way o parameterize this

Answer 22

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

Answer 23

that will give you the normal vector to the plane

Answer 24

what would i do then

Answer 25

what do you get when you do the cross product

Answer 26

gimme a sec

Answer 27

-89i+113j+189k

Answer 28

somewhat close, but that's not correct

Answer 29

what is it then?

Answer 30

try it again

Answer 31

ok