Multiplication of vectors ( Dot and Cross product).

Multiplication of vectors ( Dot and Cross product).

In this topic we will discuss about Multiplication of vectors ( Dot and Cross product), and what are the rules of dot (scalar) product and cross(vector) product ?

Before to know about this topic , students must know these topics ,

what is vector quantity? To know click here-

addition of vectors. To know click here-

resolution of vector and rectangular components of a vector . To know click here-

Multiplication of vectors ( Dot and Cross product) –

Scalar product (dot product ) of –

when the product of two vector quantity gives a scalar quantity such kind of product is called scalar product or dot product. The dot product of two vectors  and  is represented by .  ,which is equal to the product of the magnitude of the two vectors  and   and cosine of the smaller angle between them .

Example of dot product –  work done,power , flux .

Vector product ( cross product )-

When the product of two vector quantities gives the vector quantity then such quantity is called vector product. The cross  product of two vectors  and  is represented by x  ,which is equal to the product of the magnitude of the two vectors  and   and sine of the smaller angle between them .the direction of resultant vector is perpendicular to both  and .

 

Example- Torque , angular velocity,linear velocity , etc.

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