Introduction:
In computer systems, interrupt handling is an important mechanism to respond to external events or requests that require immediate attention from the processor. Vectored interrupt is a type of interrupt mechanism where each interrupt source is assigned a unique interrupt vector, which is used to determine the appropriate interrupt service routine to be executed.

Explanation:
The interrupt vector in the case of a vectored interrupt refers to an address that points to a location in memory where the beginning address of the I/O service routine is stored. This means that the correct answer is option 'C', as both options (a) and (b) are correct.

Interrupt Vector:
The interrupt vector is a data structure or a table that contains the addresses of various interrupt service routines. When an interrupt occurs, the processor uses the interrupt vector to locate the appropriate routine to handle the interrupt. The vector is typically stored in a fixed location in memory or in a special register.

Branch Information:
Option (a) mentions that the interrupt vector means the branch information from the source which interrupts the system. This implies that the interrupt vector contains information about the source of the interrupt, such as the device or component that triggered the interrupt. This information is necessary for the processor to identify the cause of the interrupt and handle it accordingly.

Address of I/O Service Routine:
Option (b) states that the interrupt vector points to a location in memory where the beginning address of the I/O service routine is stored. An I/O service routine is a specific piece of code that is executed when an interrupt occurs. It handles the input/output operations requested by the interrupt source. The interrupt vector provides the address of this routine, allowing the processor to jump to the correct location and execute the necessary code.

Conclusion:
In summary, the interrupt vector in the case of a vectored interrupt refers to an address that points to a location in memory where the beginning address of the I/O service routine is stored. It contains both the branch information from the interrupt source and the address of the corresponding service routine. This mechanism allows the processor to efficiently handle interrupts by quickly identifying the source and executing the appropriate routine.