 # MULTIPLICATION & DIVISION OF VECTOR BY A NUMBER (SCALAR)

 MULTIPLICATION & DIVISION OF VECTOR BY A NUMBER (SCALAR)
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 :
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.