Particles P and Q move in a plane with constant velocities. At time t = 0 the position vectors of P and Q, relative to a fixed point O in the plane, are (16i - 12j) m and -5i + 4j) m respectively. The velocity of P is (i + 2j) m/s and the velocity of Q

is (2i + j) m/s. Find the shortest distance between P and Q in the subsequent motion. This is an m4 question from the edexcel June 2015 paper. First I would explain to the student that I would form an equation equating the distance to the position vector of Q subtracted from the postion vector of P. Then I would tell the student that the next step is to find the square of the absolute distance by squaring the coefficient of the i and j vectors and adding them. After this the equation should be differentiated with respect to t.The differential will be equal to 0, as it is a minimum. This will be used to solve t and then the value of t will be substituted into the initial distance equation and then Pythagoras's theorem will be used to find the distance.