How to Compute the Magnitudes and Directions of Vectors
- 1). Convert the known component notation into magnitude-angle notation. For example, if you know the component a - x to be 7 and the component a - y to be 5, the magnitude of the vector A can be determined using the Pythagorean theorem. In this case, the equation becomes: √((a - x)^2 + (a - y)^2) = A = √(7^2 + 5^2) = sqrt(74) = 8.6. The magnitude of A is 8.
- 2). Determine the angle T that the vector forms with the x-axis. This is determined with the equation tan(T) = (a - y / a - x). Solving for T, the equation becomes: T = arctan(a - y / a - x) = arctan(5 / 7) = 35.5 degrees. Therefore, the vector A is inclined 35.5 degrees, counterclockwise, from the x-axis.
- 3). Determine the direction of the vector by examining its counterclockwise angle from the x-axis. For example, vector A is inclined at 35.5 degrees from the x-axis, which is moving in the positive direction, to the northeast.
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