{"id":22008,"date":"2024-01-09T15:13:52","date_gmt":"2024-01-09T09:43:52","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=22008"},"modified":"2024-01-10T17:56:49","modified_gmt":"2024-01-10T12:26:49","slug":"inter-1st-year-maths-1b-three-dimensional-coordinates-formulas","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/inter-1st-year-maths-1b-three-dimensional-coordinates-formulas\/","title":{"rendered":"Inter 1st Year Maths 1B Three Dimensional Coordinates Formulas"},"content":{"rendered":"

Use these Inter 1st Year Maths 1B Formulas<\/a> PDF Chapter 5 Three Dimensional Coordinates to solve questions creatively.<\/p>\n

Intermediate 1st Year Maths 1B Three Dimensional Coordinates Formulas<\/h2>\n

\u2192 Distance from the origin to P(x, y, z) = OP = \\(\\sqrt{x^{2}+y^{2}+z^{2}}\\)<\/p>\n

\u2192 Distance between the points P(x1<\/sub>, y1<\/sub> z1<\/sub>) and Q (x2<\/sub>, y2<\/sub>, z2<\/sub>) is<\/p>\n

\u2192 PQ = \\(\\sqrt{\\left(x_{1}-x_{2}\\right)^{2}+\\left(y_{1}-y_{2}\\right)^{2}+\\left(z_{1}-z_{2}\\right)^{2}}\\)<\/p>\n

\u2192 Translation of axes : If the origin is shifted to the point (h, k, l) under translation of axes, then x = x’ + h, y = y’ + k, z = z’ + l where (x, y, z) are the old co-ordinates and (x’, y’, z’) are the new co-ordinates.<\/p>\n

Coordinates of a Point In Space (3-D):<\/strong>
\nLet \\(\\overline{X^{\\prime} O X}, \\overline{Y^{\\prime} O Y}\\) and \\(\\overline{Z^{\\prime} O Z}\\) be three mutually perpendicular straight lines in space, intersecting at O. This point O is called origin.
\n\"Inter<\/p>\n

Axes :<\/strong>
\nThe three fixed straight lines \\(\\overline{X^{\\prime} O X}, \\overline{Y^{\\prime} O Y}\\) and \\(\\overline{Z^{\\prime} O Z}\\) are respectively called X-axis ,Y-axis and Z-axis. The three lines taken together are called rectangular coordinate axes.<\/p>\n

Coordinate Planes:<\/strong>
\nThe plane containing the axes of Y and Z is called yz-plane. Thus yoz is the yz plane. Similarly the plane zox containing the axes of z and x is called ZX-plane and the plane xoy is called the xy-plane and contains x axis and y axis.
\nThe above three planes are together called the rectangular co ordinate plane.<\/p>\n

Octants:<\/strong>
\nThe three co ordinate planes divide the whole space into 8 parts called octants.<\/p>\n

\"Inter<\/p>\n

Coordinates of A Point:<\/strong>
\nLet P be any point in the space. Draw through P , three planes parallel to the three co ordinate planes meeting the axes of X,Y,Z in the points A,B and C respectively. Then if OA = x, OB = y and OC = z, the three numbers x,y,z taken in this order are called the co ordinates of the point P and we refer the point as (x,y,z) . Any one of these x,y,z will be positive of negative according as it is measured from O along the corresponding axis, in the positive or negative direction.
\nAnother method of finding coordinates of a point.
\nThe coordinates x,y,z of a point P are the perpendicular distances of P from the three co ordinate planes YZ,ZX and XY respectively.
\n\"Inter
\nFrom fig PN = z, PL = x and PM = y
\nTherefore point P =(x,y,z)
\nNote. On YZ- plane, a point has x coordinate as zero and similarly on zx-plane y coordinates and on xy-plane z coordinates are zero.<\/p>\n

For any point on the<\/p>\n