- #1

- 584

- 0

Hello, could someone please give me some help with the following question?

Q. Determine all planes (in R³) orthogonal to the vector (1,1,1).

This is how I started off but I am not really sure how I need to go about solving this problem. I begin(by somewhat assuming that the vector (1,1,1) is perpendicular to the relevant planes) by writing the point normal form of planes with the n = (1,1,1) so I get (1,1,1).(x-p)=0.

With x = (x,y,z) I get down to [tex]x + y + z = \left( {1,1,1} \right) \bullet \mathop p\limits_\~[/tex]. With other questions I am given the point P so the dot product of the vectors 'n' and 'p' can be found. With this one the situation is different because I need to find all planes which are orthogonal to the vector (1,1,1). I thought about letting the vector p = (f,g,h) but that doesn't seem right. Could someone help me out with this one? Any help is appreciated.

Edit: My program for using Tex seems a little screwy at the moment so I had to fix part sof my post. X and p are supposed to denote vectors.

Q. Determine all planes (in R³) orthogonal to the vector (1,1,1).

This is how I started off but I am not really sure how I need to go about solving this problem. I begin(by somewhat assuming that the vector (1,1,1) is perpendicular to the relevant planes) by writing the point normal form of planes with the n = (1,1,1) so I get (1,1,1).(x-p)=0.

With x = (x,y,z) I get down to [tex]x + y + z = \left( {1,1,1} \right) \bullet \mathop p\limits_\~[/tex]. With other questions I am given the point P so the dot product of the vectors 'n' and 'p' can be found. With this one the situation is different because I need to find all planes which are orthogonal to the vector (1,1,1). I thought about letting the vector p = (f,g,h) but that doesn't seem right. Could someone help me out with this one? Any help is appreciated.

Edit: My program for using Tex seems a little screwy at the moment so I had to fix part sof my post. X and p are supposed to denote vectors.

Last edited: