7.4 Dot or Scalar product

The dot or scalar product of a
and b is denoted by a . b (read as a dot
b). It is defined as the product of magnitudes of the two
vectors and the cosine of the angle q
between them .
Thus a . b = a b cos q
, 0 £ q £ p


If a, b and c are vectors and m is a
scalar, then the following properties hold for the dot product.
1. a . b = b . a
2. a . (b + c) = a . b + a . c
3. m (a . b) = (m a) . b = a
(m b) = (a . b) m


a .a =  a ^{2}

If a and b are orthogonal (i.e.
mutually perpendicular) then a . b = 0

a. b = a b cos q Þ
cos q =

(a) Projection of a on the line of b
=
(b) Projection of b on the line of a
=

Index
7.1 Scalers & Vectors
7.2 Algebra of Vectors
7.3 Representation of a vector in a
plane
7.4 Dotor Scalar product
7.5 Polar Coordinates
Supplementary Problems
Chapter 8
