# vectors:

View Tag List
coordinate space, vector basis and operations.

## 1.02 Position: the First Vector

"Where is something" is a question persons have asked over all of time. The answer tells the "position of that something" in a mutually understood space. The "something" might be your car keys or a location such as a freeway exit or the rest room, etc. For a person to answer, "Where is it?," requires both familiarity of both persons with the surrounding space. The space "it is in" must be mutually known.

## Pharaoh's Engineers

The Great Pyramid of Egypt was constructed to precise proportions. A hypothesis is that the pyramid was constructed to fit inside an imaginary hemisphere with each of its corners and its peak touching the hemisphere. Suppose the hypothesis were true. Draw a sketch of a pyramid and calculate the angle each face makes with the horizontal plane of the desert.

## Vectors Derive Trig Laws

A typical planar triangle is shown. The triangle vertices, lengths of sides, and angles are identified by notation.

We choose to define a vector space to be the plane of the triangle. We name the two-dimensional space 0XY. We place the origin of the space at the A0B vertex of the triangle and we align its X-axis along the triangle side, 0A...

## Crank, Rod and Piston

"Power trains" are the mechanical parts by which the power of combustion is transformed into power of a rotating shaft. A sketch of a simple crank-rod-piston arrangement is shown. Engine designers must know the position of the piston face for every position of the crank. The mathematical tool, vectors, makes this task logical.