1. The vector on the line and the vector on the line associated with it are called the direction vector of the line.
2. So as long as a straight line is given, two direction vectors can be constructed (starting from the origin). That is, given the straight line ax+by+c = 0, the direction vector of the straight line L is d=(-b, a) or d=(b, -a).
3. Vertical relation, that is, Euclidean inner product of direction vector and coefficient vector is equal to zero. The coefficient vector is the normal vector of a straight line, not only a straight line, but also the normal vector of a hyperplane in N-dimensional space.
Extension: Transform the direction vector into Euler angle, rotation matrix and quaternion. In the project, the three-dimensional space direction vector needs to be transformed into a rotation matrix to represent it. The solution is as follows: input direction vector? Y 0, z0), straight line L, read the mathematical direction vector and normal vector M= (x, y, ...) at any point for a thousand times. Direction vector and normal plane oblique formula \(y=kx+bl),
Direction vector (Ioverrightarrow'S)=( 1, k), or (overrrightarrows) = (1,-cfrac(A}{B)), or n (1overrrightarrow {s} = (b,-).