A sail boat sails 2 km due East, 5 km 37o 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.

Given resultant displacement is 6 km due eastWhich may be expressed as 6i^.Given displacements are(i) 2 km due east or 2i^(ii) 5 km 37o south of east its components along x-axis =5cos⁡37∘=5×45=4i^ along y-axis =5sin⁡37∘=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^