Question

this may be easy but my head isnt working...

Find all the planes in R3 whose intersections with the xy plane is the line r(t)=t<2,1,0> @ganeshie8

Answer 1

So im thinking somewhere along the lines of 2x+y+nz=d?

Answer 2

so... its 2x+y+nz=0? @perl

Answer 3

THis is what I have so far.

We know that the point <2,1,0> is on the plane, since each plane intersects the line r = t <2,1,0>

And the equation of a plane is
n . <r - ro> = 0
where n = <a,b,c> and is perp. to plane

<a,b,c>. (<x,y,z> - <2,1,0>)

Hence the equation of the plane will look like

a(x-2) + b(y-1) + c(z-0) = 0

Answer 4

ohhhh! thank you :'\