Option 1 states that the transfer of heat energy from a heater coil to the cooking vessel takes place through convection only. However, this statement is incorrect. Convection refers to the transfer of heat energy through the movement of a fluid, such as air or liquid. In this case, since the heat energy is being transferred from the heater coil to the cooking vessel, which are both solid objects, convection alone cannot be the process of heat transfer.

Option 2 states that the transfer of heat energy takes place through conduction and convection only. This statement is also incorrect. Conduction refers to the transfer of heat energy through direct contact between two objects, while convection refers to the transfer of heat energy through the movement of a fluid. In this case, since the heat energy is being transferred from the heater coil to the cooking vessel, we can infer that conduction is the main process of heat transfer as the coil and the vessel are in direct contact. However, the statement fails to acknowledge that radiation, another form of heat transfer, may also be occurring.

Option 3 states that the transfer of heat energy takes place through radiation and convection only. This statement is correct. Radiation refers to the transfer of heat energy through electromagnetic waves, and convection refers to