The basic concept of 1. vector

(1) vector

A quantity with both magnitude and direction is called a vector. It is also called vector in physics. For example, force, velocity, acceleration and displacement are all vectors.

A vector can be represented by a directed line segment (directed line segment), the size of the vector is represented by the length of the directed line segment, and the direction of the vector is represented by the direction indicated by the arrow. A vector can also be represented by lowercase letters a, b and c, or by adding two uppercase letters (the former letter is the starting point and the latter letter is the ending point).

(5) Parallel vectors

Non-zero vectors with the same or opposite directions are called parallel vectors. Parallel vectors are also called * * * line vectors.

If vectors a and b are parallel, it is recorded as a ∨ B.

Rule: 0 is parallel to any vector.

(6) Equal vector

Vectors with the same length and direction are called equal vectors.

Vector equality has two elements: one is the same length, and the other is the same direction, both of which are indispensable.

② vectors a and b are equal, and record a = b.

③ Zero vectors are all equal.

④ Any two equal nonzero vectors can be represented by the same directed line segment, but it should be noted that the vector equality has nothing to do with the starting point of the directed line segment.

2. Pay attention to the concept of vector.

(1) vector is a quantity different from quantity, which has both magnitude and direction. No two vectors can be compared in size, only whether they are equal can be judged, but their modules can be compared in size.

(2) Vector lines are different from the directed line segments representing them. When using vector * * * lines, the directed line segments representing vectors can be parallel, not necessarily on the same straight line; A directed line segment * * * means that the line segments must be on the same straight line.

(3) According to the definition of vector equality, a vector can move in parallel at will as long as its size and direction remain unchanged. Therefore, when a vector is represented by a directed line segment, the starting point of the directed line segment can be arbitrarily selected, which also shows that any group of parallel vectors can be translated to the same straight line.

3. Algorithm of vector

(1) commutation law: α+β = β+α.

(2) Binding Law: (α+β)+γ = α+(β+γ)

(3) The distribution law of dose addition: (λ+μ) α = λ α+μ α.

(4) Distribution law of vector addition: γ (α+β) = γ α+γ β.

The above is a summary of the knowledge points of high school mathematical vector linear operation compiled by Senior Three Network, hoping to help students. c _ Kan()；