Notice that the z-coordinate of any point on the x-y plane is always 0. So, the equation z=0 can denote every point which has its z-coordinate equal to 0. That is why the equation z=0 represents the entire x-y plane! So, your answer would be (B) z=0..
Also question is, what is the vector equation of XY plane?
Similarly, the y-z-plane has standard equation x = 0 and the x-z-plane has standard equation y = 0. A plane parallel to the x-y-plane must have a standard equation z = d for some d, since it has normal vector k. A plane parallel to the y-z-plane has equation x = d, and one parallel to the x-z-plane has equation y = d.
Beside above, what is equation of a plane? If we know the normal vector of a plane and a point passing through the plane, the equation of the plane is established. Thus, the equation of a plane through a point A = ( x 1 , y 1 , z 1 ) A=(x_{1}, y_{1}, z_{1} ) A=(x1?,y1?,z1?) whose normal vector is n → = ( a , b , c ) overrightarrow{n} = (a,b,c) n =(a,b,c) is.
In this manner, what is the XY plane?
Each pair of axes defines a coordinate hyperplane. The coordinates are often denoted by the letters X, Y, and Z, or x, y, and z. The axes may then be referred to as the X-axis, Y-axis, and Z-axis, respectively. Then the coordinate hyperplanes can be referred to as the XY-plane, YZ-plane, and XZ-plane.
What is the equation of a sphere?
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.
Related Question Answers
What is vector equation of a plane?
The Vector Equation of a Plane. For example, k = (0,0,1) is a normal vector to the xy plane (the plane containing the x and y axes). Any three distinct points define our plane, or alternatively, a single point in the plane and a given normal vector to the plane.What is a normal of a plane?
In three dimensions, a surface normal, or simply normal, to a surface at point P is a vector perpendicular to the tangent plane of the surface at P. The word "normal" is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc.What is a vector equation?
General Vector Equations In general, a vector equation is any function that takes any one or more variables and returns a vector. The vector equation of a line is an equation that identifies the position vector of every point along the line.What does perpendicular to the XY plane mean?
Two-Dimensional Objects The xy-coordinate plane has two coordinate axes, the x- and y-axis. They are perpendicular to each other. A point in the xy-plane is represented by two numbers, (x, y), where x and y are the coordinates of the x- and y-axes.How do you define a plane?
A
plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.
Determination by contained points and lines
- Three non-collinear points (points not on a single line).
- A line and a point not on that line.
- Two distinct but intersecting lines.
- Two parallel lines.
What is equation of plane?
Equation of a Line. This means an equation in x and y whose solution set is a line in the (x,y) plane. The most popular form in algebra is the "slope-intercept" form. y = mx + b. This in effect uses x as a parameter and writes y as a function of x: y = f(x) = mx+b.Why is the Z axis vertical?
It is taught that the Z axis is referencing the vertical axis which is the center of rotation referred to as the axial plane. Figure 3 This denotes the rotational axis of a CNC machine. This does not however denote a moniker of X, Y or Z. The direction of the thumb is referencing axial plane.What are XYZ axis?
The xyz coordinate axis system is denoted 3. , and is represented by three real number lines. meeting at a common point, called the origin. The three number lines are called the x-axis, the y- axis, and the z-axis.What are the coordinates of the XY plane?
The origin O is the point with coordinates (0,0,0). The coordinate planes are: the xy-plane, the set of all points whose z-coordinate is zero; the yz-plane, the set of all points whose x-coordinate is zero; and the xz-plane, the set of all points whose y-coordinate is zero.Who invented Cartesian plane?
René Descartes
How are quadrants numbered?
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the (x; y) coordinates are I (+; +), II (−; +), III (−; −), and IV (+; −).Why is it called rectangular coordinate system?
Horizontal grid lines pass through the integers marked on the y-axis. The resulting grid is the rectangular coordinate system. The rectangular coordinate system is also called the x-y plane, the coordinate plane, or the Cartesian coordinate system (since it was developed by a mathematician named René Descartes.)How many dimensions does a plane have?
A plane is a flat surface with no thickness. Our world has three dimensions, but there are only two dimensions on a plane: length and width make a plane. x and y also make a plane.How do you find a point on a plane?
Set any two of your variables x,y,z to zero and solve for the other. For example, if x=0 and y=0 then the equation gives z=−D/C. So if C≠0 then a point on your plane is (0,0,−D/C). This approach gives three possible points on your plane, assuming the coefficients A,B,C are not zero.What is the XZ plane?
The xy-plane is the plane that contains the x- and y-axes; the yz-plane contains the y- and z-axes; the xz-plane contains the x- and z-axes. These three coordinate planes divide space into eight parts, called octants.At what point does the line intersect the XY plane?
The line intersect the xy-plane at the point (-10,2).What is a 3d plane called?
The 3-dimensional generalization of lines and planes is called a hyperplane (as are all of the higher-dimensional generalizations).What is the origin of a plane?
On the flat coordinate plane, there are two axes, the vertical y-axis and the horizontal x-axis. The origin is the point where they intersect. This point has the coordinates 0,0 and is usually labelled with the letter O.What is a scalar equation?
Scalar Equation of a Plane. The scalar equation of a plane, with normal vector n = (A, B, C), is Ax + By + Cz + D = 0. 
