What do you mean by resolution of a vector? What are the resolved parts called? Discuss a method to resolve a vector into two vectors in given direction? from Physics Motion in A Plane Class 11 Manipur Board
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What do you mean by resolution of a vector? What are the resolved parts called? Discuss a method to resolve a vector into two vectors in given direction?

The process of splitting up the vector into two or more vectors so that combined effect of the resultant vector is same as that of the given vectors. 
The vectors into which a given vector is split is called component of vector.

The components of a vector are also vectors. 



Let us resolve vector straight R with rightwards harpoon with barb upwards on top represented by PQ with rightwards harpoon with barb upwards on top into two vectors in the direction of A with rightwards harpoon with barb upwards on top space a n d space B with rightwards harpoon with barb upwards on top.

Draw a line from P parallel to vector straight A with rightwards harpoon with barb upwards on top and another line from Q, paralle to vector B.

We can see that the two lines intersect at point S. 

Here, PS with rightwards harpoon with barb upwards on top space parallel to A with rightwards harpoon with barb upwards on top space a n d space stack S Q with rightwards harpoon with barb upwards on top space parallel to B with rightwards harpoon with barb upwards on top 

So, we can write, 

PS with rightwards harpoon with barb upwards on top space equals space lambda A with rightwards harpoon with barb upwards on top space a n d space stack S Q with rightwards harpoon with barb upwards on top space equals beta B with rightwards harpoon with barb upwards on top 

Therefore, using triangle law of vector addition to vectors PQ with rightwards harpoon with barb upwards on top comma space stack P S with rightwards harpoon with barb upwards on top space a n d space stack S Q with rightwards harpoon with barb upwards on top, we get 

PQ with rightwards harpoon with barb upwards on top space equals space stack P S with rightwards harpoon with barb upwards on top space plus space stack S Q with rightwards harpoon with barb upwards on top
space space space space space space equals space lambda A with rightwards harpoon with barb upwards on top space plus space beta B with rightwards harpoon with barb upwards on top 

Therefore, these are the resolved components of vector straight R with rightwards harpoon with barb upwards on top in the direction of straight A with rightwards harpoon with barb upwards on top space a n d space B with rightwards harpoon with barb upwards on top.  


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Give three examples of vector quantities.

Force, impulse and momentum.
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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.
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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. 


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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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Give three examples of scalar quantities.

Mass, temperature and energy
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