Physics - Kinematics - Vectors

 Vectors

• Certain physical quantities can be described by only a numerical value or numbers completely. Such quantities are called scalar quantities. Examples of scalar quantities are speed and distance as they are related to only magnitude.\

• Some physical quantities need both direction and magnitude to be described completely. Such quantities are vector quantities. Examples are velocity and displacement. Vectors also follow the triangle law of vector addition. 

• Representation of vectors :-

                

• This is the representation of vectors diagrammatically. The front end is the head and the rear end is the tail. It is written as shown in the image above and also like this in bold letters. "AB". In this blog, we will use bold letters to represent vectors. The point where to the particle is going or moving comes after the first letter. Here, A is written before B. 

• Vectors can be shifted parallel without changing the direction

• Addition of vectors - Vectors are added by the triangle law of addition, which simply states that if a vector A is to be added to a vector B. We take A, and put the tail of B on the head of A. The line joining A and B to form a triangle is the resultant vector. For example in the question below we have to add vector A  and B :-

    `       Addition of vectors in  general. Say you have to add vector A and B which are at some angle

            from each other. Then :-

            

    

    

                Angle made with horizontal is :- 

                

• Resolution of Vectors:-   Say you have vector A inclined at an angle of 30 degrees with resect to the x-axis. Now, you can split this vector into two components, one along the x-axis and one-along the y-axis. You can add the x-axis components and y-axis components separately like normal numbers.

• Questions :-

1.