The vector is a piece with the set direction. The corner between vectors has physical value, for example when finding length of a projection of a vector to an axis.
Instruction
1. The corner between two nonzero vectors decides on the help of calculation of a scalar product. By definition the scalar product is equal to the work of lengths of vectors on a cosine of the angle between them. On the other hand, a scalar product for two vectors of a with coordinates (x1; y1) and b with coordinates (x2; y2) is calculated on a formula: ab = x1x2 + y1y2. From these two ways of finding of a scalar product it is easy to find a corner between vectors.
2. Find lengths or modules of vectors. For our vectors an and b: |a| = (x1² + y1²)^1/2, |b| = (x2² + y2²)^1/2.
3. Find a scalar product of vectors, having multiplied their coordinates in pairs: ab = x1x2 + y1y2. From definition of a scalar product of ab = |a| * |b| *cos α, where α - a corner between vectors. Then we will receive that x1x2 + y1y2 = |a| * |b| *cos α. Then cos α = (x1x2 + y1y2) / (|a| * |b|) = (x1x2 + y1y2) / ((x1² + y1²) (x2² + y2²))^1/2.
4. Find a corner α by means of Bradis's tables.
5. In case of three-dimensional space the third coordinate is added. For a vectors (x1; y1; z1) and b (x2; y2; z2) a formula for a cosine of the angle is presented in the drawing.