-->

Motion In A Plane

Question
CBSEENPH11018055

State the properties of vector addition.

Solution

The properties of vector addition are: 
(i) A vector can be added only to a vector. 
(ii) Closure property of addition: The sum of two vectors is also a vector. Hence, vectors are closed under addition.
(iii) Vector addition is commutative.
 
i.e. space straight A with rightwards arrow on top plus straight B with rightwards arrow on top space equals space straight B with rightwards arrow on top plus straight A with rightwards arrow on top

(iv)Vector addition is associative. 
 
i.e. left parenthesis straight A with rightwards arrow on top plus straight B with rightwards arrow on top right parenthesis plus straight C with rightwards arrow on top space equals space straight A with rightwards arrow on top plus left parenthesis straight B with rightwards arrow on top plus straight C with rightwards arrow on top right parenthesis 
(v) Vector addition is distributive.
i.e. space straight m left parenthesis straight A with rightwards arrow on top plus straight B with rightwards arrow on top right parenthesis space equals space straight m straight A with rightwards arrow on top plus straight m straight B with rightwards arrow on top 
(vi) Magnitude of the resultant of two vectors is less or equal to the sum of the magnitude of two vectors and greater or equal to the magnitude of the difference of the magnitude of two vectors. 
i.e. space space space space space space space parallel to right enclose straight A with rightwards arrow on top end enclose space minus space parallel to right enclose straight B with rightwards arrow on top end enclose space less-than or slanted equal to space open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space less-than or slanted equal to space open vertical bar straight A with rightwards arrow on top close vertical bar space plus space open vertical bar straight B with rightwards arrow on top close vertical bar