The difference between these two Mandarin propositions is that 向 (xiàng) can be to describe movement towards a person or location, but 往 (wáng) is only used for movement towards a location, never a person.
There is also another Mandarin preposition that describes movement towards a person or place – 朝 (cháo). This is more commonly used in writing than in conversation.
Examples Of Mandarin Prepositions
Here are a few examples wher 向 (xiàng) and 往 (wáng) can be used:
你們可以向下去。
你们可以向下去。
Nǐmen kěyǐ xiàng xiàqù.
你們可以往下去。
你们可以往下去。
Nǐmen kěyǐ wáng xiàqu.
你們可以朝下去。
你们可以朝下去。
Nǐmen kěyǐ cháo xiàqu.
You can go down there.
In the above example, since the movement is towards a place, we can any one of the three prepositions, with the provision that 朝 (cháo) would be used in a literary context.
When describing movement towards a person, either 向 (xiàng) or 朝 (cháo) can be used, with the provision that 朝 (cháo) is used in a literary context.
他向女朋友告别。
Tā xiàng nǚpéngyou gàobié.
他朝女朋友告别。
Tā cháo nǚpéngyou gàobié.
He bid farewell to his girlfriend.