Final answer:
The magnitude of a vector is found using the square root of the sum of the squares of its perpendicular components, and the direction angle is found using the arctangent of the ratio of these components.
Step-by-step explanation:
To find the magnitude and direction of a vector from its perpendicular components Ax and Ay, we can use the Pythagorean theorem and trigonometric relationships. The magnitude (A) is calculated using the equation A = √(Ax^2 + Ay^2), and the direction, given by the angle θ with respect to the x-axis, can be found using θ = tan^-1(Ay / Ax).
For example, if we are given vector components Ax = 1.20 N and Ay = 2.80 N, we calculate the magnitude as:
- Magnitude = √(1.20^2 + 2.80^2) = 3.05 N
To get the direction, we would use the arctangent function:
- Direction angle θ = tan^-1(2.80 / 1.20)
It should be noted that the actual angle will depend on the signs of Ax and Ay and may require adding 180 degrees to the calculated angle if Ax is negative, to ensure the proper direction is represented.