The rules of point multiplication and cross multiplication of vectors are derived from quaternion multiplication. Let A and B be quaternions (algebraic numbers), then the algebraic multiplication of A and B is AB = (α+AI+BJ+CK) (β+Xi+YJ+ZK) = (α+Ra) (β+Rb) = α β+α Rb+β ra-ra. α is a constant and rA is a space vector; β is a constant and rB is a space vector; Suppose I, J and K are imaginary units in three-dimensional space, I? =j？ =k？ =- 1; i j=k，j k=ⅰ，kⅰ= j； Jⅰ=-k, Kj =-ⅰ, IK =-J. Later, the application of mathematics and physics showed that the hypothesis was correct, so the hypothesis became an axiom. (1, i, j, k) is the basis of four-dimensional orthogonal spaces that are positive to each other. Quaternion multiplication includes real number multiplication, vector number multiplication, vector point multiplication and vector cross multiplication. Quaternion multiplication does not satisfy commutative law. Later, the rules of vector point multiplication and cross multiplication were refuted from quaternion algebra operation as vector algebra, vector analysis and electrodynamics alone.