Coplanar Vector

Definition:
Coplanar vectors are those which lie in the same plane. They are parallel to each other and do not intersect at any point. Coplanar vectors are used in various fields of mathematics, physics, and engineering to describe the movement and direction of objects.

Properties of Coplanar Vectors:
- Coplanar vectors have the same direction and magnitude.
- They can be added or subtracted using the parallelogram law of vector addition.
- The scalar product of two coplanar vectors is the product of their magnitudes and the cosine of the angle between them.
- The cross product of two coplanar vectors is zero.

Examples of Coplanar Vectors:
- The forces acting on an object in two dimensions.
- The velocity and acceleration vectors of a particle moving in a plane.
- The wind velocity and the velocity of an airplane moving in the same plane.

Uses of Coplanar Vectors:
- Coplanar vectors are used in physics to describe the position, velocity, and acceleration of objects moving in two dimensions.
- In engineering, coplanar vectors are used to describe the forces acting on a structure in two dimensions.
- In mathematics, coplanar vectors are used to describe the geometry of two-dimensional shapes and to find the area of a parallelogram.

Conclusion:
Coplanar vectors are vectors that lie in the same plane. They have the same direction and magnitude and can be added or subtracted using the parallelogram law of vector addition. Coplanar vectors are used in various fields of mathematics, physics, and engineering to describe the movement and direction of objects. They are an important concept in vector calculus and are used to solve many real-world problems.