Find the value(s) of a making v =6ai−3j parallel to w =a^2i+9j .

Question

a=

Answer 1

To be parallel
a^2/6a = 9/-3 = -3
a^2 = -18a
a^2 + 18a = 0
a(a+18) = 0
a = 0 or a = -18

check:
if a = 0 your vectors are <0,-3> and <0,9) which are parallel
if a = -18 your vectors are <-108,-3> and <324,9)
since <324,9> = -3<-108,-3> they are parallel