At sunrise, Ajay and Vijay are having a conversation standing in front of each other. The shadow of Vijay is formed towards the right hand of Ajay. What direction is Vijay facing?

When it is sunrise: Ajay is facing north. This is because shadows cast at sunrise point west, and since Vijay's shadow is towards Ajay's right, it indicates Ajay is facing north (and Vijay would be facing south). 

However, the important thing to notice is that Vijay's shadow is towards the right hand of Ajay, which, if Ajay faces north, means the shadow is pointing east (since the sun rises in the east). This aligns with the statement that the shadow is on Ajay's right.