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Motion in A Plane

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Physics Part I

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Physics

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The magnitude of the resultant of two vectors space straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top acting at angle straight theta is given by, 

                      space space straight R equals square root of straight P squared plus straight Q squared plus 2 PQcosθ end root

Here,       P = A + B,        Q = A - B

R e s u l t a n t space comma space straight R space equals space square root of 3 straight A squared plus straight B squared end root

therefore space P Q space equals space straight A squared space minus space straight B squared

P u t t i n g space t h e space v a l u e s space o f space straight P comma space straight Q comma space straight R space a n d space P Q space i n space a b o v e space e q u a t i o n comma space

square root of 3 straight A squared plus straight B squared end root space equals space square root of left parenthesis straight A plus straight B right parenthesis squared plus left parenthesis straight A minus straight B right parenthesis squared plus 2 left parenthesis straight A squared minus straight B squared right parenthesis space c o s theta end root

T a k i n g space s q u a r e space o n space b o t h space s i d e s comma space

space space space space space space space 3 straight A squared space plus space straight B squared space equals space left parenthesis straight A plus straight B right parenthesis squared space plus space left parenthesis straight A minus straight B right parenthesis squared space plus 2 space left parenthesis straight A squared minus straight B squared right parenthesis c o s theta

rightwards double arrow space space straight A squared space minus space straight B squared space equals 2 space left parenthesis straight A squared minus straight B squared right parenthesis c o s theta

T h a t space i s comma space c o s space straight theta space equals space bevelled 1 half

rightwards double arrow space straight theta space equals space 60 to the power of 0

                                  
                    

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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. 


814 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 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 is a vector quantity?

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