Find the components of a vector u which has initial point (-1,-2), terminal point (x,0)for some x∈ℝand which points in the same direction as (1,3)

Question

How can I find the components of this vector u? I know how to find the components of a vector when all coordinates are given (taking the coordinates of the terminal points away from the initial), but how can I go about finding the x coordinate of the terminal point?

Answer 1

$u=(x,0)-(-1,-2)=(x+1,2)$. Set this to be a multiple of $(1,3):\quad (x+1,2)=\alpha(1,3).$

Can you solve this for $x$? The answer to the question is then $x+1$.