Page 67 - Standard Handbook Of Petroleum & Natural Gas Engineering

56 Mathematics

Equation of the tangent at (x,y)
b2x,x - a2y,y = a2b2

Equations of Three-Dimensional Coordinate Systems (Figure 1-43)
Distance d between two points

- ~1 1'
d = J(x, - x1 1' + (y, - yl 1' + ( ~ 2
Direction cosines of a line
h = cos a, p = cos p, v = cos y
Direction numbers, proportional to the direction cosines with k
a = kh, b = kp, c = kv

Equations of a Plane
ax+by+cz+d=O
Intercept
x/a + y/b + z/c = 1
Normal form
hx + py + vz - p = 0
Distance from ax + by + cz + d = 0 to a point P(x,,y,,z,)
ax,+by,+c,+d

V
Figure 1-43. Three-dimensional coordinate systems.