Using a unit vector with tension.

The math in this image is describing how to calculate the unit vector of a tension force. A unit vector is a vector that has a magnitude of 1 and points in the direction of the tension force. This is useful in vector calculus, mathematical physics, engineering mechanics, statics, and dynamics. The math is as follows: $\text{Unit vector}={\displaystyle \frac{\text{Tension force}}{\Vert \text{Tension force}\Vert }}$ where $\text{Tension force}$ is the vector representing the tension force and $\|\text{Tension force}\|$ is the magnitude of the tension force. Intuitively, this means that the unit vector of a tension force is a vector that has the same direction as the tension force, but has a magnitude of 1. This makes it easy to represent the direction of the tension force in mathematical calculations.

 

The unit vector <cos(α),sin(α)> can be used to represent the direction of the tension force in any number of mathematical calculations. For example, it can be used to calculate the torque produced by the tension force, or to determine the direction of the acceleration of a particle that is being pulled by the tension force.

Here are some examples of unit vectors for different angles:

* If the tension force is pointing at an angle of 45 degrees with the positive x-axis, then the unit vector is <√2/2, √2/2>.
* If the tension force is pointing at an angle of 30 degrees with the positive x-axis, then the unit vector is <√3/2, 1/2>.
* If the tension force is pointing at an angle of 60 degrees with the positive x-axis, then the unit vector is <1/2, √3/2>.