How do you find the intersection of a sphere with an XY plane?
from the center of the sphere to the xz-plane is greater than the radius of the sphere.) To find the intersection with the yz-plane, we set x = 0: (y + 11)2+(z – 6)2 = 91,x = 0, a circle in the yz-plane with center (0,-11,6) and radius /91.
How do you know if a sphere intersects a plane?
Sphere-plane intersection When the intersection of a sphere and a plane is not empty or a single point, it is a circle. This can be seen as follows: Let S be a sphere with center O, P a plane which intersects S. Draw OE perpendicular to P and meeting P at E.
What is the equation of the YZ-plane?
z = 0
The xy-plane contains the x- and y-axes and its equation is z = 0, the xz-plane contains the x- and z-axes and its equation is y = 0, The yz-plane contains the y- and z-axes and its equation is x = 0. These three coordinate planes divide space into eight parts called octants.
What is the equation of a sphere with center x0 y0 z0 and radius r?
The equation of a sphere with center C = (x0,y0,z0) and radius r is (x x0)2 + (y y0)2 + (z z0)2 = r2.
What is the intersection of the sphere with the plane?
great circle
A great circle is the intersection a plane and a sphere where the plane also passes through the center of the sphere. Lines of longitude and the equator of the Earth are examples of great circles.
How do you find the equation of a sphere with the center and a point?
The general equation of a sphere is: (x – a)² + (y – b)² + (z – c)² = r², where (a, b, c) represents the center of the sphere, r represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.
What happens when plane intersects a sphere?
A plane can intersect a sphere at one point in which case it is called a tangent plane. Otherwise if a plane intersects a sphere the “cut” is a circle. Lines of latitude are examples of planes that intersect the Earth sphere.
When a plane intersects a sphere what must be true for the intersection to be a great circle?
If a plane intersects a sphere in hopes that the cross-section is a ‘great circle’, then the plane must also intersect the center of the sphere.
What is parallel to YZ plane?
In general, if k is a constant, then x = k represents a plane parallel to the yz-plane, y = k is a plane parallel to the xz-plane, and z = k is a plane parallel to the xy-plane.
What is the normal vector of YZ plane?
It is said that a plane is perpendicular to the yz-plane, then the plane will be parallel to the x-axis. If the planes are perpendicular, then their normals are also perpendicular. Thus the normal vector, can be said as (1, 0, 0), as the normal of the x-axis, parallel to plane and yz are perpendicular.
Which point is closest to the YZ-plane?
#10
- The xy-plane: The closest point on the xy-plane has coordinates (3,7,0), and the distance between the two points is.
- The yz-plane: The closest point on the yz-plane has coordinates (0,7,-5), and the distance between the two points is.
- The xz-plane:
- The x-axis:
- The y-axis:
- The z-axis:
How do you find the equation of a sphere?