Linear combination of vectors and RGB colours
- Simona Riva
Given three vectors u, v and w and three scalars a, b and c, the linear combination of those vectors is vector d = au + bv + cw In this applet u=(255,0,0), v=(0,255,0) and w = (0,0,255), and the scalars a, b and c range in [0,1]. Move the sliders and watch the resulting position of the linear combination vector. Now let's consider this vectorial problem from a different point of view. RGB is an additive colour model used to represent the colours of objects in many environments. In computers, a RGB colour is usually stored as a triplet of integer numbers in the range 0 to 255. (255,0,0) is red - (0,255,0) is green - (0,0,255) is blue. We can view those colours as the vectors in 3D space, having those components. Any other colour is obtained as a linear combination of these basic colours. If you multiply a vector by a scalar, you obtain the same colour, but a different shade of it. Move the sliders and find out where the yellows, or the grey shades are, and examine the position of the corresponding vector in the visual representation. Please note that the components of the resulting vector have been rounded, to match the computer requirements whenever you need to enter RGB triplets to define a colour. You can also use this applet as a reference to define dynamic colours of objects in GeoGebra.