parallel vectors

1. The problem statement, all variables and given/known data



If the vector AP parallel to u?



u= (1,4,-3)



A(-2,-1,-2)





3. The attempt at a solution



I do know that if AP is parallel to u then there must be some scalar multiple such that Ax = u.

I think it's a matter of setting up the question that I'm muddled.



Anyway, my attempt.



Let A = a₁,a₂,a₃



(a₁,a₂,a₃)(-2,-1,-2) = (1,4,3)



-2a₁= 1

-a₂=4

-2a₃ = 3



in augmented form:



-2,0,0|-1

0,2,0|-4

0,0,2|3



REF...



a₁= -1/2

a₂= -2

a₃ = 3/2