1. ## Hyperplanes

find the equation of the hyperplane in 4space which goes through the point P= (0,1,-2,3) perpendicular to the vector a= (4,3,1,-2).

our teacher never explained this and he said this was easy,.,but i am really having a hard time with this,.,thnx,.,

2. ## Re: Hyperplanes

Originally Posted by aldrincabrera

find the equation of the hyperplane in 4space which goes through the point P= (0,1,-2,3) perpendicular to the vector a= (4,3,1,-2).

our teacher never explained this and he said this was easy,.,but i am really having a hard time with this,.,thnx,.,
The equation of the hyperplane perpendicular to the vector a=(4,3,1,-2) is 4x+3y+z-2t=C

Use the fact that it passes through the point P to find C.

3. ## Re: Hyperplanes

Originally Posted by alexmahone
The equation of the hyperplane perpendicular to the vector a=(4,3,1,-2) is 4x+3y+z-2t=C

Use the fact that it passes through the point P to find C.

,.,.thnx so much,.,ammm,.,.can u please show me a sample of how i shud solve it???i'm really hanging,.,.thnx

4. ## Re: Hyperplanes

Originally Posted by aldrincabrera
,.,.thnx so much,.,ammm,.,.can u please show me a sample of how i shud solve it???i'm really hanging,.,.thnx
Just substitute the coordinates of P into the equation of the hyperplane.

5. ## Re: Hyperplanes

,,.im sorry,.,.but how shud i substitute P to the equation of the hyperplane if my problem is to find for the equation of the hyperplane???

6. ## Re: Hyperplanes

Originally Posted by aldrincabrera
,,.im sorry,.,.but how shud i substitute P to the equation of the hyperplane if my problem is to find for the equation of the hyperplane???
The equation of the hyperplane is 4x+3y+z-2t=C. Find C by substituting the coordinates of P (0,1,-2,3) into this equation.

7. ## Re: Hyperplanes

,.,.owh i get it now,.,.so C is just a number then???ammm.,.then what'll i do with C after i have it??

8. ## Re: Hyperplanes

Originally Posted by aldrincabrera
,.,.owh i get it now,.,.so C is just a number then???ammm.,.then what'll i do with C after i have it??
Then you will be able to write the equation of the hyperplane as 4x+3y+z-2t=a number

9. ## Re: Hyperplanes

,.,.thnx much,.,.

10. ## Re: Hyperplanes

,.,.what if the angle between two hyperplanes is defined as the angle between their normals, are the hyperplanes 3x + 2y + 4z - 2w = 5 and 2x - 4y + z + w = 6 orthogonal??

11. ## Re: Hyperplanes

Originally Posted by aldrincabrera
,.,.what if the angle between two hyperplanes is defined as the angle between their normals, are the hyperplanes 3x + 2y + 4z - 2w = 5 and 2x - 4y + z + w = 6 orthogonal??
The normals are (3,2,4,-2) and (2,-4,1,1) respectively. Can you find the dot product?

is it 0???

13. ## Re: Hyperplanes

Originally Posted by aldrincabrera
is it 0???
Yes. So the hyperplanes are orthogonal.

14. ## Re: Hyperplanes

,.,.thnx so much,.,.ammm,.,.can i ask another question???

15. ## Re: Hyperplanes

Originally Posted by aldrincabrera
,.,.thnx so much,.,.ammm,.,.can i ask another question???
Sure! Post it in a new thread, though.

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