Multi Flashcards
Magnitude
Unit vector
Dot product
Projection of u onto v
((uv)/(vv))v
Component of u onto v
magnitude of proj or (u*v)/||v||
cross product
<23-32, 31-13, 12-21>
parametric form
x = x0 + at …
Symmetric equations
remove t from parametric form
Tangent plane given unit vector n = <a, b, c>
a(x-x0) + b(y - y0) + c(z-z0) = 0
Velocity
Speed
Acceleration
ds/dt
Unit tangent vector
T = v / ||v||
unit normal vector
T’ (t) / ||T ‘ (t)||
a sub T (two expressions)
a * T = v * a / ||v|| = d^2/dt^2
a sub N (two expressions)
||v x a|| / ||v|| = k(ds/dt)^2
arc length
integral of speed
Curvature (K) (two expressions)
||T’(t)||/||v(t)||=||v(t) x a(t)||/||v(t)||^3
Tangent plane
dz = fx dx + fydy
Gradient
<fx, fy>
Directional derivative (Du f(x,y))
Gradient * unit vector
Direction of max increase
Gradient
Maximum value of directional derivative
||gradient||