If 1, vector A=(x 1, y 1) is perpendicular to vector B=(x2, y2), then x 1*x2+y 1*y2=0.

2. coordinate angle relationship: the inner product of a and b = | a || b | * cos (the angle between a and b) =0?

Vector verticality proves that the line plane is vertical;

Let the straight line L be a straight line perpendicular to the straight lines A and B intersecting within α, and prove that: l⊥α Proof: Let the direction vectors of A, B and L be A, B and L.

According to the basic theorem of plane vectors, any vector c in α can be written in the form of c = λ a+μ b.

∵l⊥a,l⊥b∴l a=0，l b=0

l c=l (λa+ μb)=λl a+ μl b=0+0=0∴l⊥c

Let C be the direction vector of any straight line C in α, then there is L ⊥ C. According to the arbitrariness of C, L is perpendicular to any straight line in α.

Other related properties and theorems of vectors;

1 and three-point * * * line theorem;

O is known to be a point outside the straight line where AB is located. If the vector OC is equal to the vector OA of degree k plus the vector OB of degree m, and k+m= 1, then the three points A, B and C are * * * lines;

2, center of gravity judgment:

In △ABC, if the sum of vector GB, vector GA and vector GC is 0, then G is the center of gravity of △ABC.