I tried taking the dot product of r(0) and r'(0) and setting that equal to e^0 = 1 and found that <1,0,0> DOT < a,b,c > = 1 therefore a = 1. But I'm not sure how to proceed from here.
2026-03-25 20:09:28.1774469368
Trouble Finding a Position Function Given a Dot Product & Initial Value
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The trick is in noticing that $$ \vec r\cdot \frac{d \vec r}{dt} = \frac12 \frac{d}{dt}\big(|\vec r|^2\big )$$
Can you finish?