Is it permissible to give zakat to a jobless brother who has no income, knowing that he owns an unutilized and non-agricultural plot of land, or must he sell it to pay off his debts and spend on his family from its price?

Zakat is only to be given to those who are eligible according to Islamic law. Your brother is not considered poor among those eligible for Zakat if the value of the land he does not benefit from is sufficient for him, his family, and his debts, should he sell it. However, if its price is only enough for some of his expenses, it is permissible to complete the rest of his needs from Zakat.