Saturday, November 15, 2008

Properties of scalar product

Property 1 :
The scalar product of two vectors is commutative
av.bv = bv.av

Property 2 : Scalar Product of Collinear Vectors :
(i) When the vectors av and bv are collinear and are in the same direction, then θ = 0

av.bv = |av| |bv| = ab

(i) When the vectors av and bv are collinear and are in the opposite direction, then θ = π

av.bv = |av| |bv|(-1) = -ab

Property 3 : Sign of Dot Product
The dot product av.bv may be positive or negative or zero.

(i) If the angle between the two vectors is acute (i.e., 0 < θ < 90°) then
cos θ is positive. In this case dot product is positive.
(ii) If the angle between the two vectors is obtuse (i.e., 90 < θ < 180) then
cos θ is negative. In this case dot product is negative.
(iii) If the angle between the two vectors is 90° (i.e., θ = 90°) then
cos θ = cos 90° = 0. In this case dot product is zero.

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