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7.4 Dot or Scalar product

  1. 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

  2. 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

  3. a .a = | a |2

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

  5. a. b = a b cos q Þ cos q =

  6. (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 Co-ordinates
Supplementary Problems

Chapter 8

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