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Vectors – Addition, Multiplicaton, Direction Cosines

In a Nut Shell: Vectors have magnitude and direction such as velocity and acceleration.
Vectors can be added, subtracted, and multiplied. There are two types of vector

multiplication. They are the scalar (or dot) product and the vector product.

Vector Addition U = (u₁,u₂,u₃) , V = (v₁, v₂, v₃)

1-2-3 rectangular Cartesian coordinates

Let

u₁ be the component of U along the 1 axis; v₁ be the component of V along the 1 axis

u₂ be the component of U along the 2 axis; v₂ be the component of V along the 2 axis

u₃ be the component of U along the 3 axis; v₃ be the component of V along the 3 axis

Then by vector addition (you add the components):

U +V = (u₁ + v_{1
,}u₂+v₂, u₃+ v₃ )

Magnitude of a vector U = (u₁,u₂,u₃)

U = √(u₁² + u₂²+ u₃²) (square root of the sum of its squares)

Unit Vector, e_U, is the vector divided by its magnitude. e_U = U / | U | = U / U

Definition of the Base Unit Vectors - i, j, k (along axes 1, 2, 3)

i = (1, 0, 0) j = (0, 1, 0) , k = (0, 0, 1)

Click here to continue with discussion of vectors.

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