Formula:
A and b are two vectors.
a=(a 1，a2)b=(b 1，b2).
A//b: a 1/b 1 = a2/b2 or a 1 = a2 B2 or a=λb, λ is a constant.
A vertical b: a 1b 1+a2b2 = 0.
The meaning of parallel vector:
Non-zero vectors with the same or opposite directions are called parallel (or * * * line) vectors. Vectors A and B are parallel (* * * lines), marked as A∨B, and the length of zero vector is zero, which is a vector whose starting point and ending point coincide and its direction is uncertain.
Rule: Zero vector is parallel to any vector. A set of vectors parallel to the same line is a * * * line vector. If a=(x, y) and b=(m, n), then a//b→a×b=xn-ym=0.
* * * Meaning of quantity orientation:
Three (or more) vectors parallel to the same plane are called * * * vectors. The vector in space has and only has the following two positional relationships: (1)*** plane; (2) not * * * face. Note: Only three or more vectors can speak * * * face, not * * * face.
Vector correlation definition:
1, negative vector
If the modulus of vector AB and vector CD are equal and the directions are opposite, then we call vector AB the negative vector of vector CD, which is also called the inverse vector.
2. Zero vector
A vector with a length of 0 is called a zero vector and recorded as 0. The starting point and ending point of the zero vector coincide, so the zero vector has no definite direction, or the direction of the zero vector is arbitrary.
3. Equal vector
Vectors with the same length and direction are called equal vectors. Vectors A and B are equal, and it is recorded as A = B ... Rule: All zero vectors are equal.
When the vector is represented by a directed line segment, the starting point can be arbitrarily selected. Any two equal nonzero vectors can be represented by the same directed line segment, regardless of the starting point of the directed line segment. Directed line segments with the same direction and length all represent the same vector.
4. Free vector
A vector whose starting point is not fixed can move in parallel at will, and the moved vector still represents the original vector. In the sense of free vector, equal vectors are regarded as the same vector. Only free vectors are studied in mathematics.