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Three Dimensional Geometry
CO - ORDINATES OF A POINT IN SPACE
Let O be the Origin and let OX, OY and OZ be three mutually perpendicular lines taken as x - axis, y- axis, z- axis in such a way that they form a right - handed system.
The 3 mutually perpendicular lines determine 3 mutually perpendicular planes XOY, YOZ, ZOX known as co-ordinate planes.
Plane XOY is xy-plane, YOZ is called yz-plane and ZOX is called xz-plane.
The 3 co-ordinates planes XOY, YOZ, ZOX divide the space into eight compartments known as octants.
Let P be a point in space. Through P draw planes parallel to coordinate planes meeting the axes OX, OY, OZ in points respectively. Complete the parallelopiped whose coterminous edges are OA, OB, OC.
Let OA = x, OB = y, OZ = z.
Then (x,y,z) are the co-ordinates of P.
x = distance of P from yz-plane.
y = distance of P from xz-plane.
z = distance of P from xy-plane.
Every point in yz plane has x co-ordinate 0.
Every point in xy plane has z co-ordinate 0.
every point in xz plane has y co-ordinate 0.
Any point on x- axis is of the form X,0,0.
Any point on y- axis is of the form 0,Y,0.
Any point on z- axis is of the form 0,0,Z.
Three Dimensional Geometry
CO - ORDINATES OF A POINT IN SPACE
Let O be the Origin and let OX, OY and OZ be three mutually perpendicular lines taken as x - axis, y- axis, z- axis in such a way that they form a right - handed system.
The 3 mutually perpendicular lines determine 3 mutually perpendicular planes XOY, YOZ, ZOX known as co-ordinate planes.
Plane XOY is xy-plane, YOZ is called yz-plane and ZOX is called xz-plane.
The 3 co-ordinates planes XOY, YOZ, ZOX divide the space into eight compartments known as octants.
Let P be a point in space. Through P draw planes parallel to coordinate planes meeting the axes OX, OY, OZ in points respectively. Complete the parallelopiped whose coterminous edges are OA, OB, OC.
Let OA = x, OB = y, OZ = z.
Then (x,y,z) are the co-ordinates of P.
x = distance of P from yz-plane.
y = distance of P from xz-plane.
z = distance of P from xy-plane.
Every point in yz plane has x co-ordinate 0.
Every point in xy plane has z co-ordinate 0.
every point in xz plane has y co-ordinate 0.
Any point on x- axis is of the form X,0,0.
Any point on y- axis is of the form 0,Y,0.
Any point on z- axis is of the form 0,0,Z.
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