Kollineare Vektoren prüfen | Verständlich erklärt

It explains in an understandable way how to check for collinear vectors. For two vectors to be collinear, one vector must be a multiple of the other vector. This is checked mathematically by seeing whether one vector multiplied by a parameter can produce the other vector. Explanation: Multiplying a vector by a number (scalar multiplication) merely changes the length of the vector and/or reverses the direction. If you can arrive at a different vector by simply changing the length and possibly reversing the direction of a vector, these two vectors must logically be collinear (=parallel). Since scalar multiplication is calculated row by row (coordinate by coordinate), the overall equation (vector equals parameter times vector) must be divided into three separate equations. If each equation has the same solution for the parameter, the vectors are collinear; otherwise, the vectors are not collinear.