<Dd> (c 1 a) ⋅ (c 2 b) = c 1 c 2 (a ⋅ b). (\ displaystyle (c_ (1) \ mathbf (a)) \ cdot (c_ (2) \ mathbf (b)) = c_ (1) c_ (2) (\ mathbf (a) \ cdot \ mathbf (b)).) </Dd> <Li> Not associative because the dot product between a scalar (a ⋅ b) and a vector (c) is not defined, which means that the expressions involved in the associative property, (a ⋅ b) ⋅ c or a ⋅ (b ⋅ c) are both ill - defined . Note however that the previously mentioned scalar multiplication property is sometimes called the "associative law for scalar and dot product" or one can say that "the dot product is associative with respect to scalar multiplication" because c (a ⋅ b) = (c a) ⋅ b = a ⋅ (c b). </Li> <Li> Orthogonal: <Dl> <Dd> Two non-zero vectors a and b are orthogonal if and only if a ⋅ b = 0 . </Dd> </Dl> </Li> <Dl> <Dd> Two non-zero vectors a and b are orthogonal if and only if a ⋅ b = 0 . </Dd> </Dl>

Perform dot product of matrix a and transpose of b