# What are vector projections used for?

##### 1 Answer

May 31, 2015

Vector projections are used for determining the component of a vector along a direction.

Let us take an example of work done by a force **F** in displacing a body through a displacement **d**.

It definitely makes a difference, if **F** is along **d** or perpendicular to **d** (in the latter case, the work done by **F** is zero).

So, let us for now assume that the force makes an angle

The component of **F** along **d** is **F** along **d**.

Thus, for a general case, work done is given as,

Which can be written concisely as,

**F** . **d**