You need to find coordinates of the points A and B such that:
`barOA = (x_A - x_O)bar i + (y_A - y_O)bar j`
`barOA = 2bar i- 3bar j`
You know that the coordinates `x_O` and `y_O` are 0 and 0, hence `x_A = 2` and `y_A = -3` .
`barOB = (x_B - x_O)bar i + (y_B - y_O)bar j`
`barOB = -bar i + 3bar j`
Hence, `x_B =-1` and `y_B = 3` .
You should write the equation of the line that passes through two points such that:
`(x_B-x_A)/(x-x_A) = (y_B - y_A)/(y - y_A)`
Substituting the found coordinates yields:
`(-1-2)/(x-2) = (3+3)/(y+3)`
`-3/(x-2) = 6/(y+3) =gt -1/(x-2) = 2/(y+3)`
`2(x-2) = -(y+3) =gt 2x - 4 = -y - 3 =gt 2x + y - 1 = 0`
Hence, evaluating the equation of the line AB, under given conditions, yields `2x + y - 1 = 0.`