Thread: Hyperplanes

,.good day,.,.can anyone please help me with this??

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,.,

Originally Posted by aldrincabrera

,.good day,.,.can anyone please help me with this??

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.

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

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.

,,.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???

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.

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

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

,.,.thnx much,.,.

,.,.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??

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???

Originally Posted by aldrincabrera

is it 0???

Yes. So the hyperplanes are orthogonal.

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

Originally Posted by aldrincabrera

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

Sure! Post it in a new thread, though.