A Brief Note on Coplanar Vector

Physicists use a wide variety of mathematical quantities. These words include acceleration, velocity, speed, force, work, and power. These different numbers are often referred to as “scalar” and “vector.” Vectors are a type of geometric entity with magnitude and direction. Vectors have a starting point and a terminal point that represents the point’s final position. Vectors can be subjected to various arithmetic operations, including addition, subtraction, and multiplication. We will define these words and introduce some primary vectors in the following paragraphs.

Types of vectors

There are numerous types in which we can find and describe vectors. Each of them is unique, though easy to understand. They have certain properties to describe them. 

There are eleven types of vectors. They are

• zero vector
• unit vector
• position vector
• co-initial vector
• like vector
• unlike vector
• coplanar vectors
• collinear vector
• equal vector
• displacement vector
• negative vector

Coplanar vectors 

Coplanar vectors have three or more vectors in the same plane or that can lie in the parallel plane. There is always the chance of finding any two different vectors in the same plane, which are referred to as coplanar vectors. The vector triple product of the three vectors is always equal to zero, which is another property of coplanar vectors. 

Condition for coplanar vectors

Here all the vectors lie in the same plane. For a vector to be considered coplanar, certain conditions should be followed.

For example,

• Consider three or more vectors in the 3D plane, and their scalar product is zero; then, these vectors are called coplanar vectors.
• If three vectors in the 3D plane are linearly independent, these vectors are called coplanar vectors.

Some other types of vectors

Apart from coplanar vectors, there are ten more types of vectors which are discussed below:

• Co-initial vector

 Co-initial vectors are a form of vector in which the beginning points of two or more distinct vectors are the same. All vectors in this sort of vector begin from the same point. The vectors are called co-initial vectors because their origin points are the same. 

• Collinear vectors

The collinear vector is a vector in which two or more vectors are parallel regardless of their magnitude or direction. Because they are parallel, they never cross paths.

• Zero vectors

The zero vector is a vector in which the value of the vector is zero, and the origin and endpoint points of the vector are the same. The zero vector has no constituents and will not point in any direction.

• Unit vectors

The unit vector is a subtype of a vector with a value based on the length of one unit. Unit vectors are defined as any vectors with a magnitude of one.

• Position vectors

A position vector is a vector in which the starting point is set to O, and one random point in the space is designated as A. The position vector with reference to origin O is then known as vector AO. 

•  Like and unlike vectors 

Like vectors are those that have the same direction and are referred to as such. Unlike vectors are those that have the same direction but are in opposite directions. 

• Equal vectors

Equal vectors are those vectors in which two or more vectors with the same magnitude and direction are considered equal.

• Displacement vectors

A displacement vector is that type of vector which occurs when one vector is shifted from its original position. The vector distance between the object’s starting and final points can determine the displacement.

• Negative Vector

A negative vector is a form of vector in which the value of both vectors is equal, but the direction of both vectors is opposite. Then we can write them as

 a = -b. This is known as a negative vector.  

Conclusion

Coplanar vectors are sets of vectors that lie in the same plane or are parallel to the same plane. The scalar triple product or dot product for the coplanar vectors will be 0, and they are always linearly dependent vectors.