A tracking station observes an aeroplane at two successive times to be (500, 0, 1000) and (400,

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A tracking station observes an aeroplane at two successive times to be (–500, 0, 1000) and (400, 400, 1050) relative to axes x in an easterly direction, y in a northerly direction and z vertically upwards, with distances in metres. Find the equation of the path of the aeroplane. Control advises the aeroplane to change course from its present position to level flight at the current height and turn east through an angle of 90°; what is the equation of the new path?

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