Question

A line has Cartesian equation 3x-2y+3=0 .Determine a direction vector for a line that is parallel to this line.

Could someone explain to me why the answer is
direction vector: d=(2,3)

Answer 1

Any line in two-dimensional Euclidean space can be described as the set of solutions to an equation of the form

ax + by + c = 0

where a, b, c are real numbers. Then one direction vector of (D) is (-b,a). Any multiple of (-b,a) is also a direction vector.

For example, suppose the equation of a line is 3x + 2y + 15 = 0. Then (-2,3), (-4,6), and (2,-3) are all direction vectors for this line.