Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 12

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Murray R. Spiegel: Mathematical Handbook of Formulas and Tables: Chapter 12

Published $\text {1968}$.


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$12 \quad$ Formulas from Solid Analytic Geometry

Distance $d$ between Two Points $\map {P_1} {x_1, y_1, z_1}$ and $\map {P_2} {x_2, y_2, z_2}$

$12.1$ Distance Formula in 3 Dimensions

Direction Cosines of Line Joining Points $\map {P_1} {x_1, y_1, z_1}$ and $\map {P_2} {x_2, y_2, z_2}$

Relationship between Direction Cosines

Direction Numbers

Equation of Line Joining $\map {P_1} {x_1, y_1, z_1}$ and $\map {P_2} {x_2, y_2, z_2}$ in Standard Form

Equation of Line Joining $\map {P_1} {x_1, y_1, z_1}$ and $\map {P_2} {x_2, y_2, z_2}$ in Parametric Form

Angle $\phi$ between Two Lines with Direction Cosines $l_1, m_1, n_1$ and $l_2, m_2, n_2$

General Equation of a Plane

Equation of Plane passing through Points ${x_1, y_1, z_1}$, ${x_2, y_2, z_2}$, ${x_3, y_3, z_3}$

Equation of Plane in Intercept Form

Equation of Line through ${x_0, y_0, z_0}$ and Perpendicular to Plane $A x + B y + C z + D = 0$

Normal Form for Equation of Plane

Transformation of Coordinates involving Pure Translation

Transformation of Coordinates involving Pure Rotation

Transformation of Coordinates involving Translation and Rotation

Cylindrical Coordinates $\tuple {r, \theta, z}$

Spherical Coordinates $\tuple {r, \theta, \phi}$

Equation of Sphere in Rectangular Coordinates

$12.20$: Equation of Sphere in Rectangular Coordinates

Equation of Sphere in Cylindrical Coordinates

$12.21$: Equation of Sphere in Cylindrical Coordinates

Equation of Sphere in Spherical Coordinates

$12.23$: Equation of Sphere in Spherical Coordinates

Equation of Ellipsoid with Center ${x_0, y_0, z_0}$ and Semi-Axis $a, b, c$

Elliptic Cylinder with Axis as $z$ Axis

Elliptic Cone with Axis as $z$ Axis

Hyperboloid of One Sheet

Hyperboloid of Two Sheets

Elliptic Paraboloid

Hyperbolic Paraboloid

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