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Formulas
Distance between two points:
AB = B − A =
(xB − x A )2 + ( yB − y A )2 + (zB − z A )2
Dot product (inner product) of two vectors:
u ⋅ v = u1v1 + u2v2 + u3v3 = u v cos ϕ
Angle between straight lines:
ϕ=
u ⋅v
u v
Vector product (cross product) of two vectors:
i
j k
u × v = u1 u2
v1
v2
u3 = (u2v3 − u3v2 , − u1v3 + u3v1 , u1v2 − u2v1 )
v3
Value of vector product:
u × v = u v sin ϕ
Conic sections
circle x 2 + y 2 = r 2
ellipse
x2 y2
+
=1
a 2 b2
circle ( x − m ) + ( y − n ) = r 2
2
ellipse
2
x2 y 2
+
=1
a 2 b2