Final answer:
The vector a represented by the directed line segment AB from A(4, 3) to B(0, 6) has components (-4, 3). It's found by subtracting A's coordinates from B's coordinates.
Step-by-step explanation:
To find vector a represented by the directed line segment AB where A(4, 3) and B(0, 6), we subtract the coordinates of point A from the coordinates of point B, which gives us the components of vector a. The vector a can be represented in component form as:
a = B - A = (0 - 4, 6 - 3) = (-4, 3)
This means that vector a has an x-component of -4 (indicating a move 4 units to the left on the x-axis) and a y-component of 3 (indicating a move 3 units up on the y-axis). Remember, when adding vectors or representing them graphically, such as adding them tail-to-head or finding their components, it is important to draw them to scale and find their magnitude and direction accurately with tools like rulers and protractors.