What are the characteristics of dot product?

Solution

The characteristics of dot product are:
(i) Dot product of two vectors is commutative.
Mathematically,    $straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space straight B with rightwards arrow on top times straight A with rightwards arrow on top$
(ii) Dot product is distributive.
Mathematically, $straight A with rightwards arrow on top times left parenthesis straight B with rightwards arrow on top plus straight C with rightwards arrow on top right parenthesis space equals space straight A with rightwards arrow on top times space straight B with rightwards arrow on top space plus space straight A with rightwards arrow on top times straight C with rightwards arrow on top$
(iii) Dot product of two perpendiculars vectors is zero.
Mathematically $straight A with rightwards arrow on top times straight B with rightwards arrow on top space equals space 0$ if    $straight A with rightwards arrow on top space perpendicular space straight B with rightwards arrow on top$
(iv) Dot product of vector with itself is equal to square of magnitude of vector.
Mathematically,     $straight A with rightwards arrow on top times straight A with rightwards arrow on top space equals space straight A squared$