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Explanation

A zero force member is a member of a truss that carries no load.

If three members are connected at a single joint, and two of the members are collinear, the third member is always a zero force member, so long as no external forces act on the joint. This configuration is shown in the image below.

This is because only the third member applies a force to the joint in the vertical direction, so to maintain equilibrium of forces in the vertical direction at the joint the force in that member must be zero.

This is the case at joint C, so member B-C must be a zero force member.