To define a vector in space, the system of coordinates is used. At the same time it is necessary to consider that except length (module) it is characterized also by the direction. Length of a vector can just be measured or found by means of formulas.
It is required to you
- - ruler;
- - protractor.
Instruction
1. In the simplest case to find vector length, measure length of a piece which is a vector by means of a ruler.
2. The vector in space is set by coordinates of its initial and final point. Designate coordinates of the initial point (x1; y1; z1), and final point (x2; y2; z2). To find vector length, make the following: - determine vector coordinates. For this purpose from coordinates of the initial point take away the corresponding coordinates of a final point of x=x2-x1, y=y2-y1, z=z2-z1. Receive a vector with coordinates (x; y; z); - find the sum of squares of all coordinates of a vector x²+y²+z². Take a root from the received result square. It will also be length of the considered vector.
3. In case coordinates of a vector are given at once, the task becomes simpler. If the vector is located not in space, and on the plane, then one of coordinates just cleans up; as a rule, it is z coordinate. Then length is substitution in a formula only of two coordinates. If the vector is parallel to one of axes, then its length is equal to its coordinate on an axis to which it is parallel (if coordinate is negative, take its module).
4. Sometimes for definition of a vector use its projection to an axis, and value of a corner to this axis. For example, the vector projection to an axis OH is equal h0 and it is to it at an angle α. Find vector length, having increased its projection to an axis, to a cosine of the angle under which it is d=x0 • cos(α).
5. If the vector represents the sum of two vectors, with the known lengths and a corner between them which measure by the angle meter or a protractor. Find the sum of squares of lengths of these vectors and take away the doubled work of their lengths increased by a cosine of the angle between them from the turned-out value. It will also be length of a required vector. If coordinates of vectors which sum is are known, put their corresponding coordinates, having received coordinates of a vector which is their bag, and then on coordinates find its length.