Which Plane Passes Through the Intersection Line and Satisfies Given Conditions?

[SSUP21]

Find the scalar equation of the plane which passes through the line intersection of planes x+y+z-4=0 and y+z-2= 0 that goes through (2,4,7) and satisfies the conditions
a) it is 2 units from the orgin
b) it is 3 units from the point a(5,-3,7)

I would really apprecaite if some toke me through the steps on how the solve the problem

Thank You

 

[tiny-tim]

Hi SSUP21!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[SSUP21]

Hi
and thanks for replying for this one i knew that to find a plane i needed a normal and a point
the intersection of the given planes is a vector in direction of our plane so i cross product their normals

i need another vector i had a point i needed another point so I assume that any point on the intersection of the two give planes is also on the third plane so let y = 0 and solved to find the point
then i found my second vector by doing cross product of the two point
then substituted in our given point to solve for D in equation ax + by+ cz + D=0

i have my plane but I am stuck at trying to satisfy the two conditions

 

[tiny-tim]

Hi SSUP21!

Hi
and thanks for replying for this one i knew that to find a plane i needed a normal and a point
the intersection of the given planes is a vector in direction of our plane so i cross product their normals

Yes, that's absolutely right.

i need another vector i had a point i needed another point so I assume that any point on the intersection of the two give planes is also on the third plane so let y = 0 and solved to find the point
then i found my second vector by doing cross product of the two point
then substituted in our given point to solve for D in equation ax + by+ cz + D=0

i have my plane but I am stuck at trying to satisfy the two conditions

mmm … I don't really follow what you're doing.

In fact, looking at the question more carefully, I don't really understand that either …

Find the scalar equation of the plane which passes through the line intersection of planes x+y+z-4=0 and y+z-2= 0 that goes through (2,4,7) and satisfies the conditions
a) it is 2 units from the orgin
b) it is 3 units from the point a(5,-3,7)

there's only one plane through that line that goes through (2,4,7), so what do a) and b) have to do with it??