Question

 A particle undergoes three consecutive displacements: d1 = (15 j+ 30 j+ 12 k) cm,

d2 = (23 i - 14 i -5.0 k) cm and d3 = (-13i + 15 j) cm. Find the components of the resultant displacement and its magnitude.

Answer 1

The resultant displacement

$${\bf d}={\bf d_1}+{\bf d_2}+{\bf d_3}$$ $${\bf d}=(15{\bf i}+30{\bf j}+12{\bf k})+(23{\bf i}-14{\bf j}-5.0{\bf k})\\+(-13{\bf i}+15{\bf j})=(25{\bf i}+31{\bf j}+7.0{\bf k})$$

The magnitude of resultant displacement

$$d=\sqrt{25^2+31^2+7.0^2}=40\:\rm cm$$