NEW YORK (Reuters) - The U.S. dollar fell across the board on Tuesday as optimism about a potential coronavirus vaccine and a reopening world economy helped investors shrug off Chinese-U.S. tensions, sapping demand for safe-haven assets.The U.S. Dollar Currency Index , which measures the greenback’s strength against six other major currencies, was 0.77% lower at 98.968, after slipping as low as 98.949, its weakest since May 1.Investors' increased appetite for risky assets sent stock markets..