Coinitial Vectors

Vectors are said to be coinitial when two or more vectors start from the same point. Vectors do not need to end at the same point to be coinitial. These vectors can point in the same direction (parallel) or different directions, which may cause them to intersect or diverge. For example, vectors BC and BD are coinitial if they both start at B.

Difference Between Coinitial Vectors and Collinear Vectors

To avoid confusion between coinitial and collinear vectors, keep the following differences in mind.
 

1. Coinitial vectors always begin from the same point.
2. They can have different directions and magnitudes.
3. Vectors can be added or subtracted using specific rules. In addition, you can use the triangle law, place the tail of the second vector at the head of the first, then draw a new vector from the tail of the first to the head of the second. 
4. For subtraction, change the direction of the vector being subtracted, then add. 
5. The sum of two vectors is known as the resultant vector. The resultant vector shows the total effect of all vectors together.
6. Two coinitial vectors in the same direction are parallel to each other, and in opposite directions, they are antiparallel.
7. Another way of vector addition is using the parallelogram law of vector addition. Draw both vectors starting from the same adjacent sides of a parallelogram. The diagonal starting from the same point represents the resultant vector.

From robotics to air traffic control, coinitial vectors are useful for many real-life computations across various fields. Some such applications are listed below.

• Modeling forces in physics
  When multiple forces act on the same point, they are represented as coinitial vectors. This helps in finding the resultant force and determining conditions for equilibrium. 
• Load distribution in structures in engineering
  Engineers use coinitial vectors to ensure structural stability in truss or bridge design. For instance, the forces applied at a joint are represented as coinitial vectors.
• Joint movement control in robotics
  To determine the resultant motion, multiple movement directions originating from the same joint in a robotic machine are considered coinitial vectors.
• Air traffic control
  The velocity of an aircraft and the wind effect are considered as coinitial vectors originating from the aircraft’s current location. These vectors are used to compute the resultant path.
• Character and motion collision in game development
  In 2D and 3D games, vectors originating from a character’s location are treated as coinitial to calculate trajectory and collision.