Scalar product of two vectors:

1. The scalar product of two non-zero vectors is defined as the product of the magnitude of the two vectors and cosine of the angle θ between the two vectors.

2. The dot sign is used between the two vectors to be multiplied therefore scalar product is also called dot product.

3. The scalar product of two vectors \(\overset\rightarrow{P}\) and \(\overset\rightarrow{Q}\) is given by, \(\overset\rightarrow{P}\). \(\overset\rightarrow{Q}\) = PQ cos θ where, p = magnitude of \(\overset\rightarrow{P}\), Q = magnitude of \(\overset\rightarrow{Q}\)

θ = angle between \(\overset\rightarrow{P}\) and \(\overset\rightarrow{Q}\)

4. Examples of scalar product:

i. Power (P) is a scalar product of force (\(\overset\rightarrow{F}\)) and velocity (\(\overset\rightarrow{V}\))

∴ P = \(\overset\rightarrow{F}\). \(\overset\rightarrow{V}\)

ii. Work is a scalar product of force (\(\overset\rightarrow{F}\)) and displacement (\(\overset\rightarrow{S}\)).

∴ W = \(\overset\rightarrow{F}\). \(\overset\rightarrow{S}\)