

MULTIPLICATION
OF A VECTOR BY A SCALAR 

When a vector is multiplied by a positive number (for example 2, 3 ,5, 60 unit etc.) or a scalar only its magnitude is changed but its direction remains the same as that of the original vector. If however a vector is multiplied by a negative number (for example 2, 3 ,5, 60 unit etc.) or a scalar not only its magnitude is changed but its direction also reversed. 

The product of a vector by a scalar quantity (m) follows the following rules:  

(m) = (m) which is called commutative law of multiplication.  
m(n) = (mn) which is called associative law of multiplication .  
(m + n) = m+ n which is called distributive law of multiplication .  
DIVISION
OF A VECTOR BY A SCALAR 

The division of a vector by a scalar number (n) involves the multiplication of the vector by the reciprocal of the number (n) which generates a new vector.  
Let n represents a number or scalar and m is its reciprocal then the new vector is given by :  
where m = 1/n


and its magnitude is given by:  


The direction of is same as that of if (n) is a positive number. The direction of is opposite as that of if (n) is a negative number. 