Question

A particle has its position moved from r₁ = 3i + 4j to r₂ = i + 2j. Calculate the displacement vector (Δr) and draw the r₁, r₂ and Δr vector in a two dimensional Cartesian coordinate system.

Answer 1

given, r₁ = 3i + 4j
r₂ = i + 2j
We know, displacement is the shortest distance between two points .
I mean, displacement = final position - intial position .
∴ displacement, ∆r = r₂ - r₁
∆r = i + 2j - 3i - 4j = -2i - 2j
Hence, displacement vector, ∆r = -2i - 2j

graph of r₁ , r₂ and ∆r₂ are shown in attachment,
we know, vector addition
so, r₁ + ∆r = r₂ ⇒∆r = r₂ - r₁ here it is applied to show graph.