An airplane starts from an airport located at the origin O and flies 150 km in the direction 20^o North of East to city A. From A, the airplane then flies 200 km in the direction 23^o West of North to city B. Finally, from B the airplane flies 240 km in the direction 10^o 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.