A sail boat sails 2 km due East, 5 km 370 South of East and finally an unknown displacement. If the final displacement of the boat from the starting point is 6 km due East, determine the third displacement.

(a) Given resultant displacement is 6 km due eastWhich may be expressed as 6i^Given displacement are(i) 2 km due east or 2i^(ii) 5 km 370 south of east its componentsalong x-axis = 5 cos 370 = 5×45 = 4i^along y-axis = 5 sin370 = 5×35 = -3j^(iii) unknown displacement let it be ai^+bj^∴  2i^+4i^−3j^+ ai^+bj^  =  6i^∴  6i^+ ai^−3j^+bj^  =  6i^comparing the two sidesa = 0 and b = 3∴ unknown displacement = 3j^