1、a=(x 1，y 1，z 1)、b=(x2，y2，z2)。 a * b = x 1x 2+y 1 y2+z 1z 2

2、|a|=√(x 1^2+y 1^2+z 1^2),|b|=√(x2^2+y2^2+z2^2)

3.cosθ=a*b/(|a|*|b|), and the angle θ=arccosθ.

A vector with a 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. A vector with the same direction and the same modulus is called an equal vector.

Extended data:

fundamental theorem

1, * * Linear Vector Theorem: Two space vectors A and B (B vector is not equal to 0), A∑B has a necessary and sufficient condition for a unique real number λ, so that A = λ B.

2.* * * Vector Orientation Theorem: If the two vectors A and B are not * * * straight lines, then the necessary and sufficient conditions for vector C and the surfaces of vectors A and B * * are that there is a unique pair of real numbers X, and Y makes c=ax+by.

3. Space vector decomposition theorem: If the three vectors A, B and C are not * * * planes, then there is a unique ordered real array X, Y and Z for any vector P in 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.

Baidu encyclopedia-space vector