Class Notes 
                                                                                                       
              Class: 12                                     Topic: Vectors and Three-Dimensional Geometry
               
              Subject: MATHEMATICS 
               
              Vectors 
              Physical quantities are divided into two categories: 
              1. Scalar quantities  
              2. Vector quantities  
              1. Scalar quantities – Those quantities which have only magnitude and not related to any fixed direction in the 
              space is called scalar quantities  
              Example – Mass, volume, density, work, temperature etc. 
              2. Vector quantities - Those quantities which have magnitude and as well as direction in the space is called 
              vector quantities  
              Example – Displacement, velocity, acceleration etc.  
               
              Representation of vectors  
              Vectors are represented by directed line segments and the direction of the arrow marked at one end emphasizes 
              the direction of the vector  
                                          
              A is called the initial point and B is called the terminal point  
                                                          
                                                                                             
              Types of vectors  
                                                                       
              Note – The vectors other than null vector are called proper vector  
                                                                                           
                                                                
           3. Like vectors – Vectors are called like, when they are in same 
           direction, same arrow , the magnitude may be different.
          Unlike vectors - Vectors are called unlike, when they are in same 
          direction, opposite arrow , the magnitude may be different.
                                                       
            4. Collinear or parallel vector –Two vectors are said to collinear 
            vectors, if they are parallel to the same line, irrespective to their 
            magnitudes and directions   
            5. Co-initial vector – Vectors having the same initial point are 
            called co-initial vectors 
            6. Coplanar vector – Three or more vectors are said to be coplanar, 
            if they lie in the same plane or are parallel to the same plane
                                                        
          7. Coterminous vector - Vectors having the same terminal point are 
          called coterminous vectors 
                                                    
                                                    
                              ADDITION OF VECTORS
                Triangle law of addition:
                                                                        C
                                                     A            B
              This is called triangle law of vector addition
                                                                                  
                 Components of a vector
                                               Y
                                               O         X
                                       Z