Besides scalar sizes (length, the area, volume, time, weight, etc.) which total characteristic is limited to numerical values, in physics there are vector sizes which complete description is not limited to figure. Force, speed, acceleration and some other concepts have not only the size, but also the direction. Also characterize their vector pieces or a vector.
It is required to you
- Sheet of paper, pencil, ruler.
Instruction
1. Remember what is a vector - it is the piece having the set direction. Its beginning and the end have the fixed situation, and the direction is defined from the initial point of a vector to final.
2. Designate a vector by two letters, for example OA over which put an arrow, with the edge turned into the right side. The first letter designations is the beginning of a vector, the second – its termination. Its beginning, the direction and length are considered as essential characteristics of a vector. If you do not know at least one of them, the vector becomes uncertain, and it is not possible to construct it.
3. Also do not forget what began a vector or its point of application, it is usually important by consideration of physical problems. It is not so significant for the solution of mathematical tasks. Such vectors are called free. They differ in a possibility of transfer without loss of mathematical sense from connected. At the same time the initial points of vectors combine, keeping the direction and length. For free vectors a convenient point of application – the beginning of axes of coordinates.
4. Use for creation of a vector the rectangular system of coordinates with axes of OX and OY. Vector projections to these axes are called its coordinates. They register (x, s). Respectively and the vector of OA = (x, s), at the same time its beginning coincides with the beginning of axes of coordinates. Coordinates completely characterize any free vector. On them it is possible not only to construct this vector, but also to determine its length.
5. Set to a coordinate vector. Draw axes of coordinates and construct a vector on preset values.
6. For this purpose for abscissa axes postpone value x, and for ordinate axes – value at. By means of a ruler draw the thin lines parallel to axes of coordinates through these points. Find their crossing. This point – the end of a vector.
7. Connect the beginning (it is located in the center of axes of coordinates) and the end of a vector by means of a ruler and a pencil. Designate a vector by an arrow which is drawn in its end and specifies its direction.