The quantity with size and direction in space is called space vector. The size of a vector is called the length or modulus of the vector.

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

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

A vector with the same length and opposite direction as vector A is called the inverse vector of A ... and recorded as-A.

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

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*** Metric 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.