i) The vector product of two vectors is not commutative, i.e., \(\overrightarrow { A } \times \overrightarrow { B } \neq \overrightarrow { B } \times \overrightarrow { A } \) But., \(\overrightarrow { A } \times \overrightarrow { B } =-[\overrightarrow { B } \times \overrightarrow { A } ]\)
(ii) Here it is worthwhile to note that \(|\overrightarrow { A } \times \overrightarrow { B } |=[\overrightarrow { B } \times \overrightarrow { A } ]\)= AB sin \(\theta\)  i.e., in the case of the product vectors \(\overrightarrow { A } \) \(\times\)\(\overrightarrow { B } \) and \(\overrightarrow { B } \) \(\times\) \(\overrightarrow { A } \) , the magnitudes are equal but directions are opposite to each other.

(i) By using triangular law of addition method or
(ii) Parallelogram law of vectors.

\(|3\hat { i } -2\hat { j } +\sqrt { 3 } \hat { k } |=\sqrt { { 3 }^{ 2 }+{ 2 }^{ 2 }+{ \sqrt { 3 } }^{ 2 } } \)
\(\sqrt { 9+4+3 } =\sqrt { 16 } =4\)

The length of a vector is called magnitude of the vector. It is always a positive quantity. The magnitude or norm is denoted by \(\left| \overrightarrow { A } \right| \) .

If the x, y and z axes are drawn in anticlockwise direction then the coordinate system is called as "right-handed Cartesian coordinate system".