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Motion in A Plane

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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
î and ĵ are unit vectors along x and y-axis respectively. What is the magnitude and direction of the vectors î + ĵ, and î − ĵ ? What are the components of a vector A= 2î + 3ĵ along the directions of î + ĵ and î − ĵ? [You may use graphical method]

Consider space straight a space vector space straight P with rightwards harpoon with barb upwards on top space given space as comma space

bold P bold space bold equals bold space straight i with hat on top space plus space straight j with hat on top space

straight P subscript straight x bold space straight i with hat on top space plus straight P subscript straight y space space straight j with hat on top space equals straight i with hat on top space plus space straight j with hat on top space

On space comparing space the space components space on space both space sides comma space we space get

straight P subscript straight x space equals space straight P subscript straight y space equals 1 space

open vertical bar straight P with rightwards harpoon with barb upwards on top close vertical bar space equals space square root of straight P subscript straight x squared plus straight P subscript straight y squared end root space equals space square root of left parenthesis 1 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space square root of 2 space space space space space space space space space space... space left parenthesis straight i right parenthesis

Hence comma space the space magnitude space of space the space vector space straight i with hat on top space plus space straight j with hat on top space is space square root of 2 space space space space

Let space straight theta space be space the space angle space made space by space he space vector space straight P with rightwards harpoon with barb upwards on top space comma space with space
the space straight x minus axis comma space as space shown space in space the space following space figure. space


therefore space tan space straight theta space equals space open parentheses straight P subscript straight y over straight P subscript straight x close parentheses space

rightwards double arrow space space space straight theta space equals space tan to the power of negative 1 end exponent space open parentheses 1 over 1 close parentheses space equals space 45 to the power of straight o space space space space space space space space space space space space space space... space left parenthesis ii right parenthesis
Hence comma space vector space straight i with hat on top space plus space straight j with hat on top space makes space an space angle space of space 45 to the power of straight o space with space the space straight x minus axis.

Let comma space

bold Q bold space bold equals bold space space space straight i with hat on top space minus space straight j with hat on top space

straight i. straight e. comma space straight Q subscript straight x bold space space space straight i with hat on top space minus space straight Q subscript straight y straight j with hat on top space equals straight i with hat on top space minus space straight j with hat on top space

straight Q subscript straight x space equals space space straight Q subscript straight y space space equals 1 space

open vertical bar bold Q close vertical bar space equals space square root of straight Q subscript straight x squared plus straight Q subscript straight y squared end root space equals space square root of 2 space space space space space space space space space space space space space space space space space space space space... space left parenthesis iii right parenthesis thin space

Hence comma space the space magnitude space of space the space vector space space space straight i with hat on top space minus space straight j with hat on top space is space square root of 2 space.

 
143 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 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

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

What is a scalar quantity?

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

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