I know that <2u, v> = 2<u, v> works out mathematically. But in the diagram shown above, the shadow of v that falls on u in the second case is the same length as the first case. So I cannot understand how the scaling works out in the diagram. Could you explain that?

theyComeAndGo

This is because here 2u is no longer a unit vector, so you can no longer just consider the shadow

I know that <2u, v> = 2<u, v> works out mathematically. But in the diagram shown above, the shadow of v that falls on u in the second case is the same length as the first case. So I cannot understand how the scaling works out in the diagram. Could you explain that?

This is because here 2u is no longer a unit vector, so you can no longer just consider the shadow