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.
MULTIPLICATION OF A VECTOR BY A SCALARMULTIPLICATION OF A VECTOR BY A SCALAR
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.

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