Section 1

Vectors

∣ A ∣ = A_{x}^{2} + A_{y}^{2} + A_{z}^{2}

computes the magnitude of a vector from its Cartesian components.

\overset{u}{^}_{A} = \frac{A}{∣ A ∣}

produces a vector of magnitude one with the same direction and sense as $A$ .

A = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k}

In two dimensions

A_{x} = A cos θ, A_{y} = A sin θ

R = i \sum A_{i}

By components

R_{x} = i \sum A_{i x}, R_{y} = i \sum A_{i y}, R_{z} = i \sum A_{i z}

A \cdot B = A B cos θ

Also

A \cdot B = A_{x} B_{x} + A_{y} B_{y} + A_{z} B_{z}

its result is a scalar.

A \times B = A B sin θ \overset{n}{^}

the result is perpendicular to the plane formed by $A$ and $B$ .