Properties of scalar product

Property 1 :
The scalar product of two vectors is commutative
a^v.b^v = b^v.a^v

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

a^v.b^v = |a^v| |b^v| = ab

(i) When the vectors a^v and b^v are collinear and are in the opposite direction, then θ = π

a^v.b^v = |a^v| |b^v|(-1) = -ab

Property 3 : Sign of Dot Product
The dot product a^v.b^v 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.