# Scalar equation of plane

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

## Answers and Replies

tiny-tim
Science Advisor
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
Science Advisor
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?? 