I will give my opinion, but I do not know how far you would connect all three. They are all distinctly different.
TRUST
TRUST can be looked upon as the faith reposed by one person in another. It is a human value or virtue, if you may call it so. TRUST can exist in official or private relationships. In private life, let us say that a father trusts his son so much that the son will not fall into bad company, even when the father is not closely monitoring activities. Another example can be when person A gives person B a sum of 1000 Dollars without any written agreement or any other backup, with a firm belief of getting it back without any hassles.
In official circles, let us say a person makes a travel claim and his boss simply approves it without an iota of doubt; it exhibits TRUST. In another case, a subordinate is sent for an important task that would last a few days. There is no means of communication possible. If the boss believes that the subordinate would do the job sincerely and he does so, then the TRUST is not misplaced.
Accountability
Accountability of any person is as decided by his company. The onus is on the person for the success or failure of any assignment. The performance of the person is assessed accordingly.
Motivation
Motivation can exist in official or private life. A father may motivate his daughter to become a good sportsperson. In another example, a leader may motivate his sales team to perform well against all odds.
As I mentioned at the beginning, it is up to you to connect the three.
Regards,
V. Raghunathan