Question

how to find the equation of line that has three planes that lie on it?

Answer 1

there must be a way!

Answer 2

i think..tht u must for a system with all 3 eq of planes

Answer 3

i don't know how to do!

Answer 4

http://www.netcomuk.co.uk/~jenolive/vect17.html

Answer 5

u are now working in 3dimensions so use 3 vars

Answer 6

is there a specific math problem?

Answer 7

three planes what is the line that intersects with all the planes?

Answer 8

just hold on a second

Answer 9

holding..

Answer 10

eg
x+y-z=2
3x-2y+2z
7x-3y+3z=12
TA DA!

Answer 11

^yes

Answer 12

i don't know how to do...........

Answer 13

she worked with three vars

Answer 14

yup!

Answer 15

good

Answer 16

how do i start???

Answer 17

i have a graphic calculator

Answer 18

3x-2y+2z=?????

Answer 19

Two plane intersect in line; three plane intersect at a point

Answer 20

omg! 5!

Answer 21

OMG!

Answer 22

HUH!! first of all can i clarify how do you know if those planes intersect at a point in a line or dont intersect or form a prism??

Answer 23

let me post a picture

Answer 24

okay!

Answer 25

wht if it is like this?

Answer 26

and thy keep going?

Answer 27

http://www.wolframalpha.com/input/?i=solve+the+system++x%2By-z%3D2++%3B3x-2y%2B2z%3D5++%3B+7x-3y%2B3z%3D12

Answer 28

lol im confused now as to what u want me to tell u?

Answer 29

ok those things look scary..

Answer 30

but really how do you tell by just looking at the three planes whether they're intersecting, forms a prism or joints at a point?

Answer 31

well u said tht the line is in the 3 planes---> they intersect with each other and abt the forms of planes it doesn't matter....usually it is used parallelogram

Answer 32

well if u know the slope of planars u can check by plugging in at the point where they are supposed to intersect

Answer 33

oh ya i did tell haha but what if i didn't tell how will we know??
and so how do we find the line!

Answer 34

we can divide it up into slopes of jst 3 point like i told unlike 2d graphing u now have to include the variable z as well

Answer 35

actually they all intersect at a point
\[x\to \frac{9}{5},y\to 0,z\to -\frac{1}{5}\]

Answer 36

no what if all of them are parallel to each other

Answer 37

x - y - z = 2
3 x - 2 y + 2 z = 5
7 x - 3 y + 3 z = 12
they are not parellel are they have different normal vector
{1,-1,-1}
{3,-2,2}
{7,-3,3}

Answer 38

whats normal vector?? why is it involved?

Answer 39

normal vector is analogous to slope what dealing with line in 2D

Answer 40

To describe a inclination of a plane ,we use normal vector

Answer 41

how slanted it is? whats analogous?

Answer 42

Slope of horizontal line is 0 right?

Answer 43

yup!

Answer 44

slope is another word for describing inclination of a line

Answer 45

ok so you were saying a normal vector is a vector that tells the inclination of a plane?

Answer 46

exactly

Answer 47

is there a better place where we can discuss maths it's like lagging..

Answer 48

so, want to guess what is normal vector of horizonal plane?
< , , >

Answer 49

i know! triple zero!

Answer 50

you got two out of three right
it is <0,0,1>

does not have to be 1 , can be any number

Answer 51

why is there a one because it's a line?

Answer 52

how does it tell you how sloping the plane is... hmmm they just look numbery

Answer 53

does not have to be one, but simplifies to 1
<0,0,7>
simplifies to
<0,0,1> by dividing by 7

Answer 54

hmmmmmmmmmmmm a normal vector........... is it it must be pependicular to the plane

Answer 55

you got it

Answer 56

so what if we know that the perpendicular vector?
and back to my very origninal question how do we find the line of intersection?

Answer 57

can i talk to you on msn plsssssssssssssssss

Answer 58

I don't have msn, how about twiddla

Answer 59

twitter u mean?

Answer 60

why u dont have msn! (omg)

Answer 61

http://www.twiddla.com/596692

Answer 62

how to use it looks like cool!

Answer 63

did you see me talking?

Answer 64

imran! im not done!

Answer 65

oh yeah your question about line of intersection , there is none because they intersect at a point
\[x\to \frac{9}{5},y\to 0,z\to -\frac{1}{5}\]