Final Exam Equations Flashcards
(16 cards)
1
Q
angle between u and v
A
u * v = ||u|| ||v|| cos θ
2
Q
proj v u (project of u onto v)
A
((u*v)/(||v||)^2)v
3
Q
||u x v||
A
||u|| ||v|| sin θ
4
Q
area of a parallagram
A
u * (v x w) = ||u|| ||v x w|| cos θ
5
Q
angle between planes
A
cos (θ) = (|n1*n2|)/||n1|| ||n2||
6
Q
distances between planes
A
|<x-x0, y-y0, z-z0>*n|/||n||
7
Q
arc length
A
∫√(x’(t))^2 + (y’(t))^2 + (z’(t))^2 dt or ∫ ||r’(t)|| dt = S(t)
8
Q
unit tanget
A
T(t) = r’(t) / ||r’(t)||
9
Q
one curvature fomrula
A
K = ||dT/ds||
10
Q
another curvature formula
A
K = ||(dT/dt)||/ ||r’(t)||
11
Q
Unit Normal Vector
A
N(t) = T’(t)/ ||T’(t)||
12
Q
Binormal Vector (normal vector of the osculating plane)
A
B(t) = T(t) x N(t)
13
Q
Lineralization of (x, y) at (a, b)
A
L(x, y) = fx(a, b)(x-a) + fy(a, b)(y-b) + f(a, b)
14
Q
Implicit Differation
A
dz/dx = -(df/dx)/(df/dx)
15
Q
direction derivative
A
D u f =
16
Q
A
