Question

find the values(s) of a making v=5ai-2j parallel to w=(a^2)i+6j
a = ?

I have a=0, but i can't find the second value.

Answer 1

clearly, v = ±1/3 w, so the j components line up
if v = 1/3 w, then we have
5a = 1/3 a^2
a^2 - 15a = 0
a(a-15) = 0
so a=0 or 15

If v = -1/3 w, then
-5a = 1/3 a^2
a(a+15)
a = -15 or 0