Question

Give a geometric description of the set of points: x^2+y^2+z^2-16x+10y-6z+82=0

Answer 1

de plane .... de plane ....

Answer 2

take a point in space, and produce an infinite set of vectors from the point to all other points in space. if you want to find all the vectors that are perpendicular to a specific vector, take the dot product and set it to zero

Answer 3

you might want to complete some squares to address what the normal vector is, and at what point in is anchored to in the plane:

given a point (xo,yo,zo) the set of vectors from this point are defined as:
(x-xo, y-yo, z-zo)

the subset of vectors that are perpendicular to a specific vector (a,b,c) is defined as the dot product, set to zero

(a,b,c) . (x-xo, y-yo, z-zo) = 0

a(x-xo) + b(y-yo) + c(z-zo) = 0

hmmm, i seem to have thought it too far lol .... your left with a sphere since you have x^2 y^2 z^2 parts

Answer 4

fine, the set of all vectors that are a set magnitude from a given point :)

just like x^2 + y^2 = r^2 is a circle, 3d includes an extra components ... z^2

Answer 5

yes, the answer is a sphere. i think i've figured it out (: thank you!