Applications of Vectors

Applications of Vectors

Learning Objectives:

Understand Applications of Vectors.

Applications of Vectors

Vectors have a very vast area of applications due to its easy generalize property to various topics and field of study. Vectors are constantly used in the fields of Mathematics, Physics, and Engineering etc.

Angle between two Vectors:

The angle ‘θ’ between vectors u and v can be defined by

The vectors are parallel if ‘u’ and ‘v’ are scalar multiples. The vectors are perpendicular if

Vector Projection:

The Vector Projection of a Vector ‘u’ on a nonzero vector ‘v’ is the Orthogonal Projection of ‘u’ onto a straight line parallel to ‘v’.

We use the notation . It can also be called the vector component of ‘u’ along ‘v’. The vector w2 is called the Vector Component of ‘u’ orthogonal to ‘v’. Then we use the notation .

Projection using Dot Product:

If ‘u’ and ‘v’ are nonzero vectors, then the Projection of ‘u’ onto ‘v’ is given by

Notice the projection is a scalar multiple of ‘v’.

One of the important application of vector is calculation of Work done and Force. If ‘F’ (Force) is a constant for along ‘v’, the Work Done is given by

 

Hook Questions:

1.      What are the applications of Vectors?

2.      How could you determine angle between two vectors?

3.      What is Vector Projection? How it is derived using Dot Product?

 

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