Atruck 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.

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.

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