From the figure given below we can write

It means B,C and D vectors are the components of vector A

Note that we can also write A =X +Y. So vectors X and Y are also components of vector A. It implies that we can draw any number of set of components in any desired direction.

For resolving a vector A along two directions making angles Î± and with it as shown in figure given below, we use the following:-

** AÎ± = (A sinÎ²)/(sin(Î± + Î²))**

**Perpendicular Components:****Components of Vector Formula**

Representation of any vector lying in the x – y plane, as shown in figure given below, as the sum of two vectors, one parallel to the x-axis and the other parallel to y-axis, is extremely useful in physical analysis because both have mutually independent effects. These two vectors are labeled A and A. These are called the perpendicular or rectangular component of vector A and are expressed as: **Components of a Vector**

If magnitude and direction of vector A are known then Ax = A cosÎ¸ and Ay = A sinÎ¸. Hence we can write

** Ax2 + Ay2 = A2 and tanÎ¸ = Ay/Ax**

Now, it should be clear that if we have to add 30 vectors, we will resolve each of these 30 vectors in rectangular components in any x and y direction. Then simply add all the components in the x direction and all the components in the y direction. Adding these two resultant perpendicular components will give us the final resultant.

**Illustration:**

A vector quantity of magnitude L acts on a point A along the direction making an angle of 450 with the vertical, as shown in the figure given below. Find the component of this vector in the vertical direction?

**Solution:**

The component of the vector in the vertical direction will be

** L*(cos ∏/4) = L/√2.**

Learning components of a vector is very important from IIT JEE, AIEEE and other engineering exams perspective. Most of the Physics is based on usage of **vectors and components** of vectors. Vectors and their components are also useful in trigonometry and mathematics as a whole. This is a very useful concept and should be learned thoroughly at the beginner’s level so that it paves a way for great understanding of statistics, physics and mathematics at higher levels.