Solve Plane Intersecting Lines & Parallel to X-Axis

[kaybaby]

Homework Statement

Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x - axis.

Homework Equations

The Attempt at a Solution

The equation of the plane: 4x+2kx-3y+k4y-z+kz-1-k5=0

do i then assume the plane parallel to the x-axis has points (1,0,0)?

then sub into the equation and solved k=-2

therefore the equation will be =-11y+3z-9?

 

[Susanne217]

verify that this is the method used

http://en.wikipedia.org/wiki/Plane_(geometry)#Line_of_intersection_between_two_planes

 

[rasmhop]

Homework Statement

Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x - axis.

Homework Equations

The Attempt at a Solution

The equation of the plane: 4x+2kx-3y+k4y-z+kz-1-k5=0

do i then assume the plane parallel to the x-axis has points (1,0,0)?

then sub into the equation and solved k=-2

therefore the equation will be =-11y+3z-9?

Assuming your first general equation of the planes is correct, then this method is correct. However one minor point: It sounds as though you never really showed that 0=-11y+3z-9 is parallel to the x-axis, but this is pretty trivial (you showed that if a plane of the desired form exists and that is parallel to the x-axis, then it must be this, but what if no plane of the desired form exists that is parallel to the x-axis?).