calc 3 pt1 Flashcards
1
Q
vector equations
A
<x,y,z> = <vector>t + <point></point></vector>
2
Q
angle between two vectors
A
a * b = |a| |b| cos(theta)
3
Q
equation of a plane
A
- find vector through cross product (n)
- x1(x-p1)+y1+(y-p2)+z1(z-p3) = 0
4
Q
unit tangent vector
A
T(t) = r’(t) / |r’(t)|
plug t in after first derivative
5
Q
area of a triangle
A
A = 1/2 |AB x AC|
6
Q
arc length
A
L = a > b |r’(t)|dt
7
Q
intersecting lines
A
- parallel?
- intersect?
- set x y and z of vectors to each other
- solve for t and s
- plug in x see if equal to each other
- if yes, then use t for L1 to see where they intersect
8
Q
curvature
A
K = |r’ x r”| / |r’|^3
9
Q
Elliptic Paraboloid
A
𝑧 = 𝑥2 + 𝑦2
10
Q
Hyperbolic paraboloid
A
𝑧 = 𝑥2 − 𝑦2
11
Q
Ellipsoid
A
𝑥2 + 𝑦2 + 𝑧2 = 1
12
Q
Elliptic cone
A
𝑧2 = 𝑥2 + 𝑦2
13
Q
A hyperboloid of one sheet
A
𝑧2 = 𝑥2 + 𝑦2 − 1
14
Q
A hyperboloid of two sheets
A
𝑧2 = 𝑥2 + 𝑦2 + 1
