Hi, 3 weeks its possible but you wont have much time in places as stated - youll want 2 to 3 days in vegas surely and you cant really go LV to LA via death valley without coming back on yourself a bit (enter via shoshone, leave via panamint) stay for a sunset if you can

We did san fran to yosemite to mamouth to death valley to vegas in 4 days taking it easy (300 miles aday approx)

Agree with going to yosemite - its one of the most awe inspiring places I've ever seen (2 days min needed here) glacier point at sunset is breathtaking (1/2 hour drive to top)

so much to do and see, just take your time to enjoy it and not just drive