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vector (definition)

Has both magnitude and direction

Course

Intended path (With angle and direction) of a vehicle

Drift angle

Degree of drift due to conditions (wind, etc.)

Ax/A = cosθx

Solving for angles of 3D vectors <Ax, Ay, Az>

Unit Vectors

Unit vector ú (assuming A is the original) =

i, j, k notation

(X-component)·i + (y-component)·j + (z-component)·k ***Note-All have vector signs above

Dot products

a·b = |a|·|b|·cosθ (a and b are vectors)

Parallels

U|| = (U·V)/|U| (U and V are vectors) || == parallel

Projections

Proj(v)U = ((U·V)/|V|^2)·V (read Projection of U onto v and U and V are vectors)

Perpendiculars

U⊥=U-(Proj(v)U)

U||V if Ux/Vx=Uy/Vy=Uz/Vz

How to determine whether two vectors are either parallel or anti-parallel

Center of mass

Mass1/Mass2 = Dist1/Dist2

Collinear points

Points P, Q, and R are collinear if:

m·n matrix

m--> number of rows

matrix algebra

A+B = |a11+b11, a21+b21|

x-products

UxV = (UyVz-UzVy)i-(UxVz-UzVx)j+(UxVy-UyVx)k

Finding area of a parallelogram using x-product

Area of parallelogram = magnitude of x-product of the two vectors

Triple scalar

U·(VxW) = Volume of parallelepiped (U, V, and W are vectors)

z=a+bi

Rectangular form of complex numbers

Complex conjugates

Two complex numbers of the form (a+bi) and (a-bi).

z=r(cosθ+isinθ)

Trig form of complex numbers

z·x= r(z)·r(w)·(cos(θ(z)+θ(w))+isin(θ(z)+θ(w))

Multiplying and dividing complex numbers in trig form

r(cosθ+isinθ)^n=r^n(cos(nθ)+isin(nθ))

DeMoiuve's Theorem

Odd and even functions

even--> f(-x) = f(x) (cos is even)