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.

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