1. The points S and T are midpoints of the sides AB and AD respectively of a parallelogram ABCD .The line CS and CT cut the diagonal BD at the points U and V respectively .(adsbygoogle = window.adsbygoogle || []).push({});

Show that BU = x BC + x CD and also BU = (1-y)BC +1/2 y CD , where x and y are constant.Hence show that BU=1/3 BD

Deduce that the lines CS and CT trisect the diagonal BD .

I can do the first two part but I don't know how to deduce that the lines CS and CT trisect the diagonal BD .Please help me .

2. A canal of width 2a has parallel straight banks and the water flows due north. The points A and B are on opposite banks and B is due east of A , with point O as the midpoint of AB . The x-axis and y-axis are taken in the east and north directions respectively with O as the origin. The speed of the current in the canal ,Vc is given by

Vc=Vo(1-x^2/a^2) where Vo is the speed of the current in the middle of the canal and x is the distance eastwards from the middle of the canal.A swimmer swims from A towards east at speed Vr relative to the current in the canal . Taking y to denote the distance northwards travelled by the sewimmer ,show that

dy/dx = Vo/Vr (1-x^2/a^2) .

I have no idea with this question . Is it want to find the velocity of the swimmer relative to ground ? But I cannot find the answer also if I find the velocity of the swimmer relative to ground . How to do this ?

Please help me . Thanks .:!!)

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# Vector problem ?

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