Final answer:
To find the direction angle of a vector, measure the angle it makes with the positive direction on the x-axis. The direction angle is the same as the angle formed if the vector lies in the first or fourth quadrant, but if it lies in the second or third quadrant, the direction angle is 180 degrees plus the angle formed.
Step-by-step explanation:
To find the direction angle of a vector, we need to measure the angle it makes with the positive direction on the x-axis. If the vector lies in the first or fourth quadrant, where the x-component is positive, the direction angle is the same as the angle formed. However, if the vector lies in the second or third quadrant, where the x-component is negative, the direction angle is 180 degrees plus the angle formed.
For example, if the vector has components Ax = 3 and Ay = -4, we can use the inverse tangent function to find the angle formed: tan^(-1)(|-4/3|) = tan^(-1)(4/3) ≈ 53.1 degrees. Since Ax is positive, the direction angle is also 53.1 degrees.