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 :
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.