The vector represents the directed piece. Addition of two vectors is made as by means of a geometrical or analytical method. The result of addition is measured in the first case after construction, in the second – pays off. The new vector is result of addition of two vectors.
It is required to you
- - ruler;
- - calculator.
Instruction
1. To construct the sum of two vectors, by means of parallel translation combine them so that they proceeded from one point. Through the end of one of vectors draw the straight line parallel to the second vector. Through the end of the second vector draw the straight line parallel to the first vector. The constructed straight lines will be crossed in some point. At the correct construction, a vector and pieces of straight lines between the ends of vectors and a point of intersection will give a parallelogram. Construct a vector which beginning will be in a point of combination of vectors, and the end in a point of intersection of the constructed straight lines. It will be the sum of two these vectors. Measure length of the received vector by a ruler.
2. If vector are parallel and sent to one party, then measure their lengths. Postpone a piece parallel to them which length is equal to the sum of lengths of these vectors. Send it to the same party, as initial a vector. It will also be their sum. If vector are sent to the opposite directions, take away their lengths. Construct a piece, parallel to vectors, direct it towards a bigger vector. It will be the sum of opposite directed parallel vectors.
3. If lengths of two vectors and a corner between them are known, find the module (absolute value) of their sum without making construction. Count the sum of squares of lengths of vectors of an and b, and add to it their doubled work increased by a cosine of the angle α between them. Take a root from the received number square c= √ (a²+b²+a∙b∙cos(α)). It will be length of a vector equal to the sum of vectors of an and b.
4. If vector are set by coordinates, find their sum, having put the corresponding coordinates. For example, if the vector of a has coordinates (x1; y1; z1), b vector (x2; y2; z2), having put term by term coordinates, receive a vector of c which coordinates (x1+x2; y1+y2; z1+z2). This vector will also be the sum of vectors of an and b. When vector are in a case on the plane, do not consider the coordinate of z.