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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
Find the magnitude and direction of resultant of two vectors without using the parallelogram of vector addition.

Let space straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top be two vectors acting at angle straight theta.

straight R with rightwards harpoon with barb upwards on top space is the resultant of straight P with rightwards harpoon with barb upwards on top space a n d space Q with rightwards harpoon with barb upwards on top

Therefore, straight R with rightwards harpoon with barb upwards on top space equals space P with rightwards harpoon with barb upwards on top space plus space Q with rightwards harpoon with barb upwards on top 



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Let, the resultant straight R with rightwards harpoon with barb upwards on top make angle straight alpha with OA with rightwards harpoon with barb upwards on top.

straight R with rightwards harpoon with barb upwards on top. P with rightwards harpoon with barb upwards on top space equals space stack left parenthesis P with rightwards harpoon with barb upwards on top space plus Q with rightwards harpoon with barb upwards on top right parenthesis space. space P with rightwards harpoon with barb upwards on top
R P space cos space alpha space equals space P with rightwards harpoon with barb upwards on top. P with rightwards harpoon with barb upwards on top space plus space Q with rightwards harpoon with barb upwards on top. P with rightwards harpoon with barb upwards on top
R P thin space cos space alpha space equals space P squared space plus space P Q space cos theta space space space space space space space space space space space space space space... space left parenthesis 1 right parenthesis space

Also, 

open vertical bar straight R with rightwards harpoon with barb upwards on top cross times straight P with rightwards harpoon with barb upwards on top close vertical bar space equals space open parentheses P with rightwards harpoon with barb upwards on top plus Q with rightwards harpoon with barb upwards on top close parentheses cross times P with rightwards harpoon with barb upwards on top space

R P space sin space alpha space equals space open vertical bar P with rightwards harpoon with barb upwards on top cross times P with rightwards harpoon with barb upwards on top space plus space Q with rightwards harpoon with barb upwards on top cross times P with rightwards harpoon with barb upwards on top close vertical bar

R P space cos alpha space equals space P Q space sin space theta space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis space

D i v i d i n g space e q u a t i o n space left parenthesis 2 right parenthesis space b y space left parenthesis 1 right parenthesis comma space w e space h a v e

fraction numerator R P space sin alpha over denominator R P space cos space alpha end fraction space equals space fraction numerator P Q space sin space theta over denominator P squared space plus space P Q space cos theta end fraction space

i. e. comma space tan alpha space equals space fraction numerator Q space sin theta over denominator P space plus space Q cos theta end fraction

space space space space space space space space space space

Thus, for two vectors acting in the same direction, the magnitude of the resultant vector is equal to the sum of the magnitude of two vectors and acts along 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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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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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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