If |C|^2 = 60 and C × (î + 2ĵ + 5k) = 0, then a value of C ⋅ (-î + 2ĵ + 3k) is :

C is parallel to î + 2ĵ + 5k.
→ C = t(î + 2ĵ + 5k), where 't' is a scalar.
|C|^2 = 60 → t^2(î.î + 4ĵ.ĵ + 25k.k) = 60 → 60 = t^2 × 30 → t = ±√2
Now C ⋅ (-î + 2ĵ + 3k) = ±√2(î + 2ĵ + 5k) ⋅ (-î + 2ĵ + 3k) = ±√2[-1 + 4 + 15] = ±12√2