2. When one is incapable of using water, even when it is available

For example, a sick and/or an eldery person who cannot move and has no one to help him/her perform  https://www.al-feqh.com/en/wudu-ablution" rel="nofollow - wudu ’.

3. When one fears he will be harmed by using water

Examples include:

a- A sick person whose use of water (for pruificaton) may aggravate his sickness;

b- A person experiencing extreme cold and does not have the means to warm water, coupled with a strong fear that he may fall sick from the use of cold water.

This is because the Prophet ﷺ approved of the action of Amr Ibn Al-‘As when he led his people in prayer and he had performed at-tayammum due to the extreme cold.[ narrated by Abu Dawud.]

c-Someone far away from others or on a long journey with no water except a little for him to drink and he is not able to get other water.
source: https://www.al-feqh.com/en/tayammum-dry-ablution