How to build a vector?
A vector is usually called a segment that hasspecified direction. Both the beginning and the end of the vector have a fixed position, with the help of which the direction of the vector is determined. Let us consider in more detail how to construct a vector with given coordinates.
- Draw a coordinate system (x, y, z) in space, mark single segments on the axes.
- Set aside on the two axes the required coordinates, draw from them the dotted lines parallel to the axes, to the intersection. Learn the point of intersection, which you need to connect the dotted line with the origin.
- Draw a vector from the origin to the resulting point.
- Set aside on the third axis the desired number, through this point draw a dotted line that will be parallel to the constructed vector.
- From the end of the vector draw a line dotted line parallel to the third axis until it intersects with the line from the previous point.
- Finally, connect the origin and the resulting point.
Sometimes it is required to construct a vector, which is the result of addition or subtraction of other vectors. Therefore now we will consider operations with vectors, we learn how to add and subtract them.
Operations on a vector
Geometric vectors can be addedin several ways. So, for example, the most common way of adding vectors is the triangle rule. To add two vectors according to this rule, it is necessary to arrange the vectors parallel to each other in such a way that the beginning of the first vector coincides with the end of the second one, and the third side of the resulting triangle will be the sum vector.
You can also calculate the sum of the vectors by the ruleparallelogram. Vectors should start from one point, parallel to each vector, you must draw a line so that the resulting parallelogram is obtained. The diagonal of the constructed parallelogram will be the sum of these vectors.
To subtract two vectors, we need to add the firstvector and vector, which will be the opposite of the second. For this, the rule of the triangle is also used, which has the following formulation: the difference of vectors that are transferred in such a way that their beginnings coincide is a vector whose beginning coincides with the end of the subtrahend vector, and also with the end of the decremented vector.