Scalar (or dot) product of two vectors Assignment Help

Vectors - Scalar (or dot) product of two vectors

Scalar (or dot) product of two vectors:

The scalar product of 1387_Addition of two vectors9.png and 1147_Addition of two vectors10.png, written as 1387_Addition of two vectors9.png.1147_Addition of two vectors10.png, can be defined to be the |1387_Addition of two vectors9.png|cosθ where θ is angle between the vectors 1387_Addition of two vectors9.png and 1147_Addition of two vectors10.png i.e. 1387_Addition of two vectors9.png = abcosθ.

 

Geometrical Interpretation:

 194_Scalar (or dot) product of two vectors.png

1387_Addition of two vectors9.png.1147_Addition of two vectors10.png is  product  of  length of  one  vector  and  length of the projection of the  other  vector  in the  direction of former.

1387_Addition of two vectors9.png.1147_Addition of two vectors10.png= |1387_Addition of two vectors9.png| Projection of |1147_Addition of two vectors10.png| in direction of 1387_Addition of two vectors9.png =|1147_Addition of two vectors10.png|.Projection of 1387_Addition of two vectors9.png in direction of |1147_Addition of two vectors10.png|

Properties:

580_Scalar (or dot) product of two vectors1.png

 

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