Vector is a bridge to transform geometric problems into algebraic problems, and the addition and subtraction of vectors are geometric operations by algebraic methods.
Triangle rule solves the problem of vector addition: connect each vector from beginning to end in turn, and the result is that the starting point of the first vector points to the end point of the last vector.
Parallelogram rule solution
The method of vector addition: two vectors are translated to the common starting point, and the two sides of the vector are regarded as parallelograms, and the result is the diagonal of the common starting point.
The parallelogram rule is used to solve the method of vector subtraction: two vectors are translated to a common starting point, and both sides of the vector are used as parallelograms, and the result points from the endpoint of the subtracted vector to the endpoint of the subtracted vector (the parallelogram rule is only applicable to the addition and subtraction of two non-zero non-* * * line vectors).
When learning vectors, you can follow the following steps:
1. Definition of learning vector: A vector is a quantity with a size and a direction, which is mathematically represented by an arrow. The length of the arrow indicates the size of the vector, and the direction of the arrow indicates the direction of the vector.
2. Basic operations of learning vectors: addition, subtraction, number multiplication, point multiplication, etc. The operation of addition and subtraction is to add and subtract the length and direction of a vector. The operation method of number multiplication is to multiply the length of the vector by a real number, and the direction remains the same. The operation of dot multiplication is to add the length products of two vectors to get a scalar.
3. Graphical representation of drawing vectors: you can use arrows to represent vectors, the length of arrows indicates the size of vectors, and the direction of arrows indicates the direction of vectors, so that you can represent vectors more vividly.
4. Coordinate representation of learning vectors: a vector can be represented by coordinates, a two-dimensional vector can be represented by two numbers, and a three-dimensional vector can be represented by three numbers.
5. Relevant formulas of learning vectors: such as the module length of vectors, the included angle of vectors, the projection of vectors, etc. Mastering these formulas is helpful to solve related problems.
6. Doing related topics of vectors: After mastering the basic knowledge, you need to practice doing related topics of vectors, consolidate what you have learned and improve your problem-solving ability.