Your cousin has just retired and the family is gathering for a packing party to prepare her to move from Auckland to the Bay of Islands. (a) When walking to her place, you traverse four successive displacements as below: d1 = (−63i) m d2 = (−40 cos 40◦i − 40 sin 40◦j) m d3 = (+30 cos 50◦i− 30 sin 50◦j) m d4 = (−50j) m where i indicate east, j indicates north and the angles of 40◦ and 50◦ are angles to the east-west direction. (i) Sketch a map of the four successive displacement vectors.