A truck is traveling due north at 30 km/hr approaching a crossroad. On a perpendicular road a police car is traveling west toward the intersection at 40 km/hr. Both vehicles will reach the crossroad in exactly one hour. Find the vector currently representing the displacement of the truck with respect to the police car.

Answer: Ok, we can put the truck on a x-axis and the police car on the y-axis.

if the truck has a velocity of 30km/h and in an hour will be in the intersection, then it has a 30km distance to the intersection, who will be our 0 in our graph. so truck vector is (30km, 0)

where a vector is of the form (x, y)

for the police car is the same, it has 40km distance to the intersection, but in the y-axis, so the vector is (0,40km)

so the vector representing the displacement of the truck with respect of the police car is the difference of both vectors

it is (30km, - 40km)

if you want a more precise, you can write the vector of the form

(30 km - 30km/h*t, 40 km - 40km/h*t) where t is time.

this second vectors takes in account how the position of the vehicles changes as the time goes.