## Physics XI Content

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

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MULTIPLICATIONOF 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 . | |||

DIVISIONOF 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. |