# Hyperplanes

Show 40 post(s) from this thread on one page
Page 1 of 2 12 Last
• Jun 23rd 2011, 02:54 AM
aldrincabrera
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,.,
• Jun 23rd 2011, 03:02 AM
alexmahone
Re: Hyperplanes
Quote:

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.
• Jun 23rd 2011, 03:05 AM
aldrincabrera
Re: Hyperplanes
Quote:

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
• Jun 23rd 2011, 03:07 AM
alexmahone
Re: Hyperplanes
Quote:

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.
• Jun 23rd 2011, 03:13 AM
aldrincabrera
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???
• Jun 23rd 2011, 03:16 AM
alexmahone
Re: Hyperplanes
Quote:

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.
• Jun 23rd 2011, 03:26 AM
aldrincabrera
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??
• Jun 23rd 2011, 03:28 AM
alexmahone
Re: Hyperplanes
Quote:

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
• Jun 23rd 2011, 03:35 AM
aldrincabrera
Re: Hyperplanes
,.,.thnx much,.,.
• Jun 23rd 2011, 03:39 AM
aldrincabrera
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??
• Jun 23rd 2011, 03:45 AM
alexmahone
Re: Hyperplanes
Quote:

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?
• Jun 23rd 2011, 04:00 AM
aldrincabrera
Re: Hyperplanes
is it 0???
• Jun 23rd 2011, 04:05 AM
alexmahone
Re: Hyperplanes
Quote:

Originally Posted by aldrincabrera
is it 0???

Yes. So the hyperplanes are orthogonal.
• Jun 23rd 2011, 05:15 AM
aldrincabrera
Re: Hyperplanes
,.,.thnx so much,.,.ammm,.,.can i ask another question???
• Jun 23rd 2011, 05:18 AM
alexmahone
Re: Hyperplanes
Quote:

Originally Posted by aldrincabrera
,.,.thnx so much,.,.ammm,.,.can i ask another question???

Sure! Post it in a new thread, though.
Show 40 post(s) from this thread on one page
Page 1 of 2 12 Last