Question

define dot product in physics .give one example

Answer 1

Dot product is the product of magnitudes of 2 vectors with the Cosine of the angle between them. You can take the smaller or the larger angle between the vectors. That is if theta is the angle then you can take (360-theta) as well.

Geometrically, it will also be equal to (read it slowly) the product of “projection” of magnitude of one vector on the other and the magnitude of the 2nd vector.

In Physics, as an example, Mechanical Work is a scalar and a result of dot product of force and displacement vectors. Like-wise, Magnetic flux is the dot product of magnetic field and vector area

Answer 2

The dot product, also called the scalar product, of two vector s is a number (scalar quantity) obtained by performing a specific operation on the vector components. The dot product has meaning only for pairs of vectors having the same number of dimensions. The symbol for dot product is a heavy dot (

In the two-dimensional Cartesian plane, vectors are expressed in terms of the x-coordinates and y -coordinates of their end points, assuming they begin at the origin ( x , y ) = (0,0). Some examples are shown in the illustration below.



The dot product of two vectors is determined by multiplying their x -coordinates, then multiplying their y -coordinates, and finally adding the two products. Thus, in the above example:

A  B = (2 x -4) + (5 x -3) = -8 - 15 = -23

B  C = (-4 x 5) + (-3 x -5) = -20 + 15 = -5

C  A = (5 x 2) + (-5 x 5) = 10 - 25 = -15

In polar coordinates, vectors are expressed in terms of length (magnitude) and direction. When expressed in this format, the dot product of two vectors is equal to the product of their lengths, multiplied by the cosine of the angle between them.

For any two vectors A and B , A  B = B  A . That is, the dot product operation is commutative; it does not matter in which order the operation is performed.