A tunnel is to be evacated through a hill. In order to define position, coordinates (x,y,z) are taken relative to an origin O such that x is the distance east from O, y is the distance north and z is the verticl distance upwards, with one unit equal to 100m. The tunnel starts at point A(2,3,5) and runs in a straight line in the direction i+j-0.5k.
b) an old tunnel through the hill has equation r=4i+j+2k+x(7i+15j+0k). Show that the point p on the new tunnel where x=7.5 is directly above a point Q in the old tunnel. Find the separation PQ of the tunnels at this point.