Impact on the U.S. dollar: usually positive
An increase in U.S. Treasury yields makes dollar-denominated assets more attractive to investors seeking returns, which increases demand for the dollar and strengthens it against other currencies. This is a key principle in the theory of "interest rate differentials".
Impact on gold: usually negative
Gold is a non-yielding asset. When bond yields rise, the "opportunity cost" of holding gold increases, because holding bonds becomes more attractive than gold, which does not provide periodic income. Also, the strength of the dollar (as mentioned) makes gold more expensive for holders of other currencies, which reduces global demand.
But there are important complexities:
If the increase in yields is driven by genuine inflation concerns (not just a rate hike), gold may still hold its strength as a hedge against inflation despite higher nominal yields. What matters here is the real return (Real Yield = nominal yield − inflation), not nominal yield alone.
If rising yields coincide with market turmoil or fears of a recession, investors may turn to gold as a safe haven despite higher yields, weakening this traditional inverse relationship.
The speed of the rise matters too: a sudden, sharp increase creates a stronger negative shock to gold than a gradual, expected rise.
In short: the theoretical relationship is inverse between bond yields and gold, and direct between yields and the dollar, but the context (inflation, growth, geopolitical risks) can significantly alter this relationship.
This is general analysis, not investment advice. I am not a licensed financial advisor.