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Definition, Properties, Solved Example Problems - Scalar Product of Two Vectors | 11th Physics : Kinematics

Chapter: 11th Physics : Kinematics

Scalar Product of Two Vectors

The scalar product (or dot product) of two vectors is defined as the product of the magnitudes of both the vectors and the cosine of the angle between them.

Scalar Product of Two Vectors

Definition

The scalar product (or dot product) of two vectors is defined as the product of the magnitudes of both the vectors and the cosine of the angle between them.

Thus if there are two vectors  and  having an angle θ between them, then their scalar product is defined as    = AB cos θ. Here, A and B are magnitudes of  and .

Properties

The product quantity    is always a scalar. It is positive if the angle between the vectors is acute (i.e., < 90°) and negative if the angle between them is obtuse (i.e. 90°<θ< 180°).




The work done is basically a scalar product between the force vector and the displacement vector. Apart from work done, there are other physical quantities which are also defined through scalar products.

 

Solved Example Problems for Multiplication Of Vector By A Scalar





Solved Example Problems for Scalar Product of Two Vectors





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11th Physics : Kinematics : Scalar Product of Two Vectors | Definition, Properties, Solved Example Problems


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