Find the slope of the vector v = ai + bj. The slope of a vector is a/b.
Flip the fraction of the vector's slope and change its polarity to find the slope of the line perpendicular to it. For example, if the vector's slope is 2/3, the new slope would be -3/2. You can confirm that these slopes are perpendicular because 2/3 x -3/2 = -1.
Plug your new slope values into the equation of a line. So for a slope of -3/2, the equation of the line becomes y = -3/2x + b, where "b" is the y-axis intercept, or 3x + 2y = c.