Virtual classroom can be a greater place of collaboration when students are given "write" access to the whiteboard. By enabling, "write" access to the whiteboard, it is found that generally students are very careful about what they write there (the awareness that class is being recorded might have added to this carefulness). Since virtual classroom whiteboard already has built-in ways to draw/type circles, ellipses, lines, rectangles, co-ordinate axes, text etc., one can manage to draw/type with mouse with occasional need to use free-hand feature. However, those students who want to go a step further with free-hand usage can try pen mouse / pen tablet which is a simple device that can be connected to the PC via USB. Availability of brands may depend on the place, but in India, "iBall" is worth mentioning and, "Wacom" should be available in many places globally. Some models also have wireless mouse besides pen but it is not required as the earlier mouse continues to work. The pen itself can be a partial replacement of conventional mouse after getting accustomed to it.
A man starts walking from the point P (-3, 4), touches the x-axis at R, and then turns to reach at the point Q (0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50 [(PR)^2 + (RQ)^2 ]$ is equal to _ _ _ _ . Solution For time to be minimum at constant speed, the directions must be symmetric. In other words, the angles made by PR and RQ with the vertical must be the same just like in the law of reflection in optics. $tan \theta = \frac {MP}{MR} = \frac {NQ}{NR} $ $\Rightarrow \frac {3-r}{4} = \frac {r}{2}$ $\Rightarrow r=1 $ So, $R \equiv ( - 1,0)$ Now, $50(PR^2+RQ^2)=50[(4+16)+(1+4)]=1250$