Vertical plane

The vertical plane is one of two planes. $X Z$ ${\ displaystyle XZ}$ ${\ displaystyle XZ}$ or $Y Z$ ${\ displaystyle YZ}$ $Yz$ in a Cartesian coordinate system that is perpendicular to the horizontal plane $X Y$ ${\ displaystyle XY}$ $Xy$ . In this plane $X Z$ ${\ displaystyle XZ}$ ${\ displaystyle XZ}$ perpendicular to the axis $O Y$ ${\ displaystyle OY}$ $Oy$ , and the plane $Y Z$ ${\ displaystyle YZ}$ $Yz$ perpendicular to the axis $O X$ ${\ displaystyle OX}$ $Ox$ .

Cartesian coordinate system

Horizontal Equation

Like all other planes, vertical planes $X Z$ ${\ displaystyle XZ}$ and $Y Z$ ${\ displaystyle YZ}$ are first-order algebraic surfaces and in a Cartesian coordinate system can be defined by equations of the first degree.

Since the general equation of the plane has the form

Ax+By+Cz+D=0\qquad

{\ displaystyle Ax + By + Cz + D = 0 \ qquad}

Where $A, B, C$ ${\ displaystyle A, B, C}$ and $D$ ${\ displaystyle D}$ - constant; then if:

in the vertical plane $X Z$ ${\ displaystyle XZ}$ take values $A=0$ ${\ displaystyle A = 0}$ , $C=0$ ${\ displaystyle C = 0}$ , then the equation of the vertical plane takes the trivial form: $y=D$ ${\ displaystyle y = D}$ where the quantity $D$ ${\ displaystyle D}$ determines the distance from the origin O (0,0,0) to the plane $X Z$ ${\ displaystyle XZ}$ ;
in the vertical plane $Y Z$ ${\ displaystyle YZ}$ take values $C=0$ ${\ displaystyle C = 0}$ , $D=0$ ${\ displaystyle D = 0}$ , then the equation of the vertical plane takes the trivial form: $x=D$ ${\ displaystyle x = D}$ where the quantity $D$ ${\ displaystyle D}$ determines the distance from the origin O (0,0,0) to the plane $Y Z$ ${\ displaystyle YZ}$ .

Literature

Ilyin V.A., Poznyak E.G. Analytical geometry. - M .: FIZMATLIT, 2002 .-- 240 p.

Vertical plane

Horizontal Equation

Literature

See also

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