Determine the equation of the plane which distance to the origin is equal to 3 and passing through the intersection of the planes x+y+z-11 = 0 and

x-4y+5z-10=0

Help please!

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- Oct 19th 2012, 08:07 PMbastianteVector Geometry
Determine the equation of the plane which distance to the origin is equal to 3 and passing through the intersection of the planes x+y+z-11 = 0 and

x-4y+5z-10=0

Help please! - Oct 19th 2012, 09:29 PMchiroRe: Vector Geometry
Hey bastiante.

Can you show us what you have tried? (Hint: If it goes through both planes then the area of intersection will be where P1 = P2 or Plane1 = Plane2). - Oct 19th 2012, 10:33 PMMaxJasperRe: Vector Geometry
Equation of system of planes containing the line of intersection of the two planes:

Expanding and collecting terms planes are:

Distance of point (0,0,0) from these planes:

Solve to find k={1, -47/139}. Hence equation of two planes with distance 3 and containing line of intersection of the two given planes are:

and:

NB.: Check the 2 planes if both are solutions(Shake) - Oct 20th 2012, 11:30 AMbastianteRe: Vector Geometry
Thank you very much! I did not know that equation for intersection of two planes