Were blue whales alive when the dinosaurs were alive?

It's not likely, but it's possible they could be descendants of dinosaurs. For instance, most of today's lizards and birds are descendants of dinosaurs. There were also dinosaurs who lived in the waters, like whales do today, and they were very big. So yes, whales might be descendants of dinosaurs, but are technically not dinosaurs themselves because seemingly all dinosaurs became extinct a long time ago.