vector geometry

[ggcheck]

1. The problem statement, all variables and given/known dataFind all planes in R^3 whose intersection with the xz-plane is the lijne with equation 3x + 2z = 5

3. The attempt at a solution
Very confused here, not sure how to start it. the xz plane is another way of saying y = 0... which I'm guessing is why the equation doesn't have a y term. what is the best way to proceed?

[dynamicsolo]

The xz plane is another way of saying y = 0... which I'm guessing is why the equation doesn't have a y term.


Your surmise is correct.

Think about the given line, which has the direction vector <3, 0, 2>. Pick a point on this line. Any plane you are interested in finding contains this line, so any vector perpendicular to its direction vector is the normal vector to one of those planes. What must those vectors look like? What would be the coefficients for the planes for which those are the normal vectors? What planes with those coefficients contain the point on 3x + 2z = 5 that you chose?

[ggcheck]

I'm still pretty confused

[ggcheck]

a point that satisfies 3x + 2z = 5 must also satisfy 0x + 1y + 0z = 0 and some other equation... so we need to find this other equation? how?

[ice109]

can you find at least one plane whose intersection with xz plane is that line?

[ggcheck]

uhhh

[HallsofIvy]

1. The problem statement, all variables and given/known dataFind all planes in R^3 whose intersection with the xz-plane is the lijne with equation 3x + 2z = 5

3. The attempt at a solution
Very confused here, not sure how to start it. the xz plane is another way of saying y = 0... which I'm guessing is why the equation doesn't have a y term. what is the best way to proceed?

Any plane can be written Ax+ By+ Cz= D for some A, B, C, D. you are correct that in the xz plane, y= 0. So saying that the plane intersects the xz plane in the line 3x+ 2z= 5, means that when y= 0, Ax+ Cz= D is the same as 3x+ 2z= 5. What are A, C, and D? What about B? (Remember that there are an infinite number of planes that intersect the xz plane in that line.)

[ggcheck]

Ax + Cz = 5?

cause A and c can be any numbers but D = 5?

ugh

[ice109]

no A=3 , C=2 , D=5 and B can be any number

[ggcheck]

3x + 2z = 5 is the solution??? It's that simple?

[ggcheck]

3x + ny + 2z = 5

this is it, yes?

[Essenar]

I know this is pretty old, but I'm on the same problem and I'm stuck as well.

You say there's infinite planes that intersect with that line, but what exactly is the question asking for then?

It says "Find all planes in R^3", if there's infinite planes then what am I writing?

This is the last problem on my homework and I'm really confused about what it's asking for.