A charged particle A repels another charged particle B with a force of constant magnitude F0 acting along a line that makes angles α, β, and γ with the x, y, and z axes respectively.
(i) Express the force FAB in terms of F0 and the direction cosines.
(ii) Derive the vector expression for the force exerted by particle B on particle A.
(iii) Show that the algebraic sum of the corresponding components of the two forces along each axis is zero.
(iv) Discuss how this result illustrates the vector nature of Newton’s third law when forces act along an arbitrary oblique line in three–dimensional space.