Can you solve (5,8,12) = s(1,1,1)+t(1,2,3) for s and t? In other words does point (5,8,12) lie on the plane through the origin that is spanned by the vectors (1,1,1) and (1,2,3).
I'm new with vectors and not really sure where to start. I don't understand the question, how do 2 vectors compose a plane?
The most general, basic and indeed simple rule is: two vectors in are equal iff their entries are equal correpondingly.
Thus, for example,
That's how we knew that, for instance,
The rest is the definition of how to sum vectors and multiply them by scalars: you MUST have studied this otherwise you wouldn't receive exercises like the one you asked about.
Tonio