An airplane starts from an airport located at the origin O and flies 150 km in the direction 20o North of East to city A. From A, the airplane then flies 200 km in the direction 23o West of North to city B. Finally, from B the airplane flies 240 km in the direction 10o South of West to city C.
i. Sketch a figure representing the complete journey, using the vectors a = -OA→, b = -AB→, c = --BC→.
ii. Give the components of a, b and c in the (O, i,j) coordinate system, where i and j are unit vectors along the East and North directions, respectively.
iii. Express the location of city C as a vector r = -OC→ and find the distance from O to C.