Year 12s: what will be the first way you research your future options? >>

A question about planes ._.

Wikiwa

How do i express the plane : r = (2 , 1 , 1)+ :biggrin:

(1 , 1 , 0) + :wink:

(0 , 0 , 1)
in Cartesian form =/

Reply 1

pyrolol

The 'simplest' (in terms of knowledge) method is just to write r = (x, y, z); then to take the vector equation as 3 simultaneous equations, and eliminate the two variables you don't want (the :biggrin:

and

in your post).

You can also go via an equation of the form r.n = d, or once you get more familiar with them you'll be able to write out simple ones like that directly, but the above is the basic solution.

Reply 2

Wikiwa

the problem i have is that the 3 equations i get are x= 2 + :biggrin:

; y= 1+

; z= 1+

and since i suck i dont know how to eliminate those two variables.

Reply 3

JXPES

Well you can easily get a relationship between x and y. z can be any value.

Reply 4

generalebriety

Wikiwa

the problem i have is that the 3 equations i get are x= 2 + :biggrin:

; y= 1+

; z= 1+

and since i suck i dont know how to eliminate those two variables.

Eliminate

to get a relationship between x and y. The parameter :wink:

isn't actually relating z to either of x or y here (and of course nor is :biggrin:

), which implies that z is independent of x and y, and so won't show up in the resulting equation. :smile:

If it helps, consider a simpler problem: find the Cartesian equation of the line r = (2, 1) + :p:

(0, 1). (But before you do that, draw it so that it's obvious what the answer's going to be.)

Reply 5

Wikiwa

really o.o? thats the answer? z can be any value? so i just write x-y=1? bah i was thinking about z being any value in the bus >_>

Reply 6

THE STUDENT RUSE

i came here in search of a discussion about jet engines

Reply 7

Wikiwa

i came here in search of a discussion about jet engines

lol :P sry for misleading tittle

Reply 8

divine_alive

THE STUDENT RUSE

i came here in search of a discussion about jet engines

me too

Reply 9

Diaz89

Bloody hell, I got a brain freeze by the second post

Reply 10

Theconomist

I came here to tell you all I kknew about commercial airplanes :s-smilie:

Reply 11

Unbiased Opinion

What the ****? You can use :biggrin:

and

in maths?!

Reply 12

nuodai

OP, if you find a vector (say, ( :smile:

) ) which is perpendicular to both (1,1,0) and (0,0,1) then dotting both sides with it will give you something in the form ( :smile:

) · (x,y,z) = (2,1,1) · ( :smile:

) [the other two vectors on the RHS disappear because they're perpendicular to the vector you've dotted them with]. Expanding both sides of this gives you an equation in Cartesian form.

Unbiased Opinion

What the ****? You can use :biggrin:

and

in maths?!

There's no reason why not... what makes letters so special?