Final answer:
To write the matrix equation as a vector equation, decompose the vector into its x and y components. Then, use the beginning and end coordinates to find Ax and Ay. These components help determine the vector's magnitude and direction.
Step-by-step explanation:
To use the definition of ax to write the matrix equation as a vector equation, we must consider that a vector à in a rectangular coordinate system can be represented as à = AxÎ + AyÍ + Azᴢ. Now, when you decompose a vector into its components along the x- and y-axes, you get the components Ax and Ay, respectively.
The scalar components Ax and Ay can be found if you know the coordinates of the beginning point b(x, yb) and the end point e(xe, ye) of the vector, by subtracting the origin point coordinates from the end point coordinates: Ax = xe - xb, Ay = ye - yb.
Considering vector à and its components Ax and Ay, they will form a right triangle as per the given information. This relationship is crucial for determining the magnitude A and the direction of vector à from its components Ax and Ay, relative to the x-axis.