Physics

Problem

A particle moves from point

A(x_1,y_1)

to point

B(x_2,y_2)

in a two-dimensional rectangular coordinate system. (a) Derive an expression for the displacement vector

\Delta \mathbf r

in unit-vector form. (b) Hence show that the magnitude of this displacement is

|\Delta \mathbf r| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}