# Scalar equation of plane

## Main Question or Discussion Point

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
Homework Helper
Hi SSUP21! Show us what you've tried, and where you're stuck, and then we'll know how to help! 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 im stuck at trying to satisfy the two conditions

tiny-tim
Homework Helper
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 im 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?? 