Vectors                                          

 

 

Example:  Find the scalar projection of  U  and  of  V given by:

 

             U  =  i  +  j   +  k       and     V =  3 i  +  4  j

 

          V  =  √ [ (3)2  +  (4)2 ]  =  √5

 

         compV U  =   U  · V  /  V   =  [ (1)(3) + (1)(4) ]  /   5  =   7 / 5    (result)

 

 

.    

 

Example:  Find the vector projection of  U  onto  V given by:

 

             U  =  i  +  j   +  k       and     V =  3 i  +  4  j

 

          V  =  √ [ (3)2  +  (4)2 ]  =  5

 

  Recall       projV U  =   ( U ∙ V )  eV

 

 

        U  · V  =  (1)(3)  +  (1) (4)  =  7,       U  · V  /  V   =   7 / 5   

           eV    =   ( 3 i  +  4  j ) /  5

 

     projV U  =   ( U ∙ V )  eV    =     (7 / 25) [ 3i + 4j ]   (result)

 

 

 

 

 

Example:  Determine which of the following expressions are meaningful.

 

 

1.    ( A ∙ B )  ∙  C      Not meaningful  A ∙ B  is a scalar  and scalar product is between

                                  two vectors.

 

2.  ( A ∙ B )  C          Meaningful  since  A ∙ B  is a scalar and you can multiply a scalar

                                 times a vector. 

 

3.    ( A ∙ B )  +   C   Not meaningful since  A ∙ B  is a scalar  and  C  is a vector

 

 

 

                  

 



Copyright © 2017 Richard C. Coddington

All rights reserved.