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# Vector equation of plane example watch

1. If anyone could help with this please:

I'm looking at an example where you are asked to find the vector equation of the plane which contains points P with pos vector

r = (x,y,z) and satisfies the equn x + 2y + z = 4.

For the solution, it starts by saying 'Observe that (4,0,0) lies on this plane. So take r(0) = (4,0,0).

How do they get (4,0,0)?

2. 4 + 2*0 + 0 = 4, so (4,0,0) satisfies the equation, so is on the plane.
3. Im guessing they just picked a simple point to start with, i.e. set two variables (y and z in this case) to 0 and looked at what the other (x) must be. Equally valid should be points like (0,2,0) (from x = z = 0) or (0,0,4) (from x = y =0). But this is just a guess and there could be more to it than that - please correct me anyone!
4. (Original post by Scipio90)
4 + 2*0 + 0 = 4, so (4,0,0) satisfies the equation, so is on the plane.
(Original post by spread_logic_not_hate)
Im guessing they just picked a simple point to start with, i.e. set two variables (y and z in this case) to 0 and looked at what the other (x) must be. Equally valid should be points like (0,2,0) (from x = z = 0) or (0,0,4) (from x = y =0). But this is just a guess and there could be more to it than that - please correct me anyone!
Thanks to both of you for explaining.

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