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Fundamentals of Stress and Vibration 1. Mathematics for Structural mechanics
[A Practical guide for aspiring Designers / Analysts]
[Fig 1.30: scalar product - vector resolution]
By similar argument, work done for vectors ( a ) onto ( b ) is also given by:
Work done = a b cosθ
Expanding the above expression, we get:
Work done = a . b + a . b = a b cosθ
y
x
x
y
The above expression is a Scalar quantity.
Therefore, when two vectors are multiplied in a certain way, we get a scalar quantity and is called
‘Scalar product’ of vectors. This is formally represented as:
a . b = a b cosθ ----- Scalar product of Vectors
To summarize: The Scalar/Dot product is a product of vectors, that gives us a scalar quantity.
This product is used while computing scalar quantities like energy, power, work done, angular
displacement, etc.
Example: let us consider two vectors ( a ) and ( b ), in the ‘x-y’ plane, as shown in [Fig 1.31] .
Find the magnitude and direction of the vector resulting from addition of vector ( b ) from ( a ).
[Fig 1.31: Vectors on an ‘x-y’ plane]
QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 31
