The vector is characterized not only the absolute length, but also the direction. Therefore "to fix" it in space various systems of coordinates are used. Exactly knowing coordinates of a vector it is possible to determine its length by special mathematical formulas.
It is required to you
- - system of coordinates;
- - ruler;
- - protractor.
Instruction
1. If the vector is on the plane, then its beginning and the end have coordinates (x1; y1), (x2; y2). To find its length make the following mathematical operations:: 1. Find vector coordinates for what from coordinates of the end of a vector, we take away coordinates of the beginning of x=x2-x1, y=y2-y1.2. Square each of coordinates and find their sum x²+y². 3. Take a root from the number received at implementation of item 2 square. It will also be length of the vector located on the plane.
2. In that case if the vector is located in space, it has three coordinates x, y and z which are calculated by the same rules, as for the vector located on the plane. Find its length, having put squares of all three coordinates, and take from result of addition a root square.
3. If one of coordinates of a vector and a corner between it and an axis OH (if the corner between an axis of OY and a vector to find a required corner is known, take away it from 90º) is known, find length from ratios which characterize polar coordinates: 1. length of a vector is equal to the relation of coordinate x to a cosine of this corner; 2. length of a vector is equal y coordinate relations to a sine of this corner.
4. To find length of a vector which represents the sum of two vectors find its coordinates, having put the corresponding coordinates, and then find length of a vector which coordinates are known.
5. If coordinates of vectors are unknown, and only lengths are known, transfer one of vectors so that it began in that point where the second comes to an end. Measure a corner between them. Then from the sum of squares of lengths of vectors take away their doubled work increased by a cosine of the angle between them. Take a root from the received number square. It will also be length of a vector which is the sum of two vectors. Construct it, having connected the beginning of the second vector to the end of the first.