What is the Cartesian equation of the XY 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.
Which plane is parallel to the XY plane?
This is the vertical plane that is parallel to the xz-plane and five units to the right of it as in Figure 7(b). 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.
Which axis is perpendicular to XY plane?
View of xy plane, z -axis is perpendicular to the sheet.
What plane is perpendicular to YZ?
The plane paraellel to YZ – plane is perpendicular to X-axis.
How do you prove a plane is parallel to the XY-plane?
Standard equations for some special planes. 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.
What does perpendicular to the XY plane mean?
The (cartesian) equation of a plane is linear in the coordinates x and y, that is, of the form ax+by+cz+d=0. The plane is vertical (perpendicular to the xy-plane) if c=0; it is perpendicular to the x-axis if b=c=0; and likewise for the other coordinates.
How do you specify YZ plane?
∵ x coordinate gives the distance of a point from yz plane. ∴ x = 0 implies that the point lies on yz plane. Thus, locus of a point for which x = 0 is the yz plane or we can say that equation of yz plane is x = 0.
How do you show a vector is perpendicular to a plane?
A plane defined via vectors perpendicular to a normal. Thus, given a vector ⟨a,b,c⟩ we know that all planes perpendicular to this vector have the form ax+by+cz=d, and any surface of this form is a plane perpendicular to ⟨a,b,c⟩.