Write v in the form v = ai + bj

Question

If vector v has an initial point at P1 and a terminal point at P2, write v as multiples of the basis vectors i=⟨1, 0⟩j=⟨0, 1⟩ That is, write v in the form v = ai + bj.
P₁ = (0, −2), P₂ = (0, 45) and v = ?

a) v = 0i − 43j
b) v = 0i + 43j
c) v = 0i − 47j
d) v = 0i + 47j

Answer 1

To find the vector we subtract the initial point from the terminal point:

 v = P2 - P1 = (0, 45) - (0, -2) = (0, 47)

So  v = 0i + 47j   Answer d).