From Linear Algebra, using MATLAB

Dot and Cross Products Theory: Two non-zero vectors a and b in R' are parallel if and only if their cross product is the zero vector of R3. In this case, there exists a unique line passing through the origin and parallel to the vector a (or b): r(t)-t-a , where t E (-o,to). If two non-zero vectors in R'are not parallel, there exists a unique plane parallel to the given vectors and passing through the origin. The plane is defined by a normal vector n -axb and the current vector v = [x, y, z]. The equation of the plane is L(x, y, z) = 0 , where L(x, y, z)-dot(n, v). In this exercise, you will **Create a function in MATLAB function [] = dotcross(a,b) which takes as inputs nonzero vectors a and b. The function has to verify if the vectors are parallel. If this is the case, the function outputs: (1) a message that a and b are parallel; (2) a message 'The line through the origin parallel to vector a (or b) is, ; (3) the line r(t) itself: r(t)-t-a