The size of a vector is called its length or modulus.

1. A vector with a length of 0 is called a zero vector and recorded as 0.

2. A vector with a modulus of 1 is called a unit vector.

3. A vector with the same length and opposite direction as vector A is called the inverse vector of A. Write it as-a..

4. Vectors with equal directions and equal modules are called equal vectors.

fundamental theorem

1, * * * line vector theorem

Two space vectors a and b (b the b vector is not equal to 0), and the necessary and sufficient condition for A∑b is that there is a unique real number λ, so that a = λ b.

2.* * * Vector-oriented Theorem

If the two vectors A and B are not * * * lines, the necessary and sufficient condition for the * * plane of vector C and vectors A and B is that there exists a unique pair of real numbers X and Y, so that c=ax+by.

3, space vector decomposition theorem

If the three vectors A, B and C are not * * * planes, there is a unique ordered real array X, Y and Z for any vector P in the space, so that p=xa+yb+zc.

Three vectors of any non-* * plane can be used as the basis of space, and the representation of zero vector is unique.