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Class 10 Class 12
State the properties of vector addition.

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

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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


814 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views