What must user program be prohibited from writing to the memory locations containing the interrupt vector?

An interrupt vector is the memory address of an interrupt handler, or an index into an array called an interrupt vector table that contains the memory addresses of interrupt handlers. When an interrupt is generated, the Operating System saves its execution state via a context switch, and begins execution of the interrupt handler at the interrupt vector. An interrupt handler, also known as an interrupt service routine (ISR), is a callback subroutine in operating system whose execution is triggered by the reception of an interrupt. Interrupt handlers have a multitude of functions, which vary based on the reason the interrupt was generated and the speed at which the interrupt handler completes its task. 

An interrupt handler is a low-level counterpart of event handlers. These handlers are initiated by either hardware interrupts or interrupt instructions in software, and are used for servicing hardware devices and transitions between protected modes of operation such as system calls.
If some program access the memory address used by interrupt vector then some interrupt may be disturbed or missed. So, this is completely unknown to operating system and hence no prevention mechanism is there and system may go into crash.