Learning Objectives:

__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 **w _{2}** is called the

*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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