A
sphere is the set of all points in space equidistant from a fixed point, the center of the sphere (
[link] ), just as the set of all points in a plane that are equidistant from the center represents a circle. In a sphere, as in a circle, the distance from the center to a point on the sphere is called the
radius .
The equation of a circle is derived using the distance formula in two dimensions. In the same way, the equation of a sphere is based on the three-dimensional formula for distance.
Rule: equation of a sphere
The sphere with center
$\left(a,b,c\right)$ and radius
$r$ can be represented by the equation
Let
$P=\left(\mathrm{-5},2,3\right)$ and
$Q=\left(3,4,\mathrm{-1}\right),$ and suppose line segment
$PQ$ forms the diameter of a sphere (
[link] ). Find the equation of the sphere.
Since
$PQ$ is a diameter of the sphere, we know the center of the sphere is the midpoint of
$PQ.$ Then,
Describe the set of points in three-dimensional space that satisfies
${\left(x-2\right)}^{2}+{\left(y-1\right)}^{2}=4,$ and graph the set.
The
x - and
y -coordinates form a circle in the
xy -plane of radius
$2,$ centered at
$\left(2,1\right).$ Since there is no restriction on the
z -coordinate, the three-dimensional result is a circular cylinder of radius
$2$ centered on the line with
$x=2\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}y=1.$ The cylinder extends indefinitely in the
z -direction (
[link] ).
Just like two-dimensional vectors, three-dimensional vectors are quantities with both magnitude and direction, and they are represented by directed line segments (arrows). With a three-dimensional vector, we use a three-dimensional arrow.
Questions & Answers
Preparation and Applications of Nanomaterial for Drug Delivery
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
can you provide the details of the parametric equations for the lines that defince doubly-ruled surfeces (huperbolids of one sheet and hyperbolic paraboloid). Can you explain each of the variables in the equations?