I need help to find a non-zero vector x in R^3 that belongs both to span {y; u} and to span {v;w} where y = (1; 0; 0); u = (0; 0; 1), v = (1; 1; 1) and w = (2; 3;-1).
Thank you.
Let 'a' be the required vector.
you need to satisfy box[a,y,u]=0 and box[a,v,w]=0; where box[a,y,u] is the scalar triple product of a, y and u.
Since span of two given vectors is a plane, 'a' lies on the intersection of two planes hence 'a' is the vector along the line of intersection of the two planes.