A car is driven 30km west and then 80 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

Answer 1

If you arrive at point denoted by the vector p,
p = -30i + (-80/√2i - 80/√2j)
p = -30i + (-56.57i - 56.57j)

p = -86.57i - 56.57j
|p| = 103.41

tanθ = -56.57/-86.57 = 0.653
θ = 213.16°