From now on, the vector of space will always be represented by a directed line segment. It can be said that the vectors of space are equal as long as they have the same direction and magnitude, unlike the numbers you have dealt with so far. In other words, any vector in space can be replaced by a vector in space that is parallel to it and has the same magnitude, and from this, the vector in space can move freely without changing its direction and magnitude..
First, we define two elementary operations, vector addition and scalar multiplication, for a vector in space. The operation of creating the sum of vectors is called addition, and multiplying the vector by a constant is called scalar multiplication.
When orthogonal coordinates are prepared for the space vector and the origin and end points are translated so that the starting point is the origin. The vector connecting the origin and end coordinates is or expressed as .Especially when dealing with -space, a vector created by connecting points with the origin as the starting point. Using , .Then the sum of two vectors , is defined by
Also, the magnitude of the vector is the distance of the line segment connecting origin and point , which is represented by .
Basic vector
Vector formed by connecting the origin and the point is called the basic vector in the Cartesian coordinate system . Also, a vector with a magnitude of 1 such as is called a unit vector.