## 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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