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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

Find the area of triangle whose vertices are straight P left right arrow left parenthesis 1 comma space 1 comma space 1 right parenthesis comma space straight Q left right arrow left parenthesis 2 comma space 2 comma space 2 right parenthesis space and space straight R left right arrow left parenthesis 2 comma space minus 1 comma space 2 right parenthesis.


Here, P, Q and R are the vertices of a triangle.

Therefore PQ with rightwards arrow on top space and space PR with rightwards arrow on top represent the sides of triangle as shown in the figure.

              

We have, 

PQ with rightwards arrow on top space equals space left parenthesis 2 minus 1 right parenthesis straight i with hat on top plus left parenthesis 2 minus 1 right parenthesis straight j with hat on top plus left parenthesis 2 minus 1 right parenthesis straight k with hat on top space equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top 

PR with rightwards arrow on top space equals left parenthesis 2 minus 1 right parenthesis straight i with hat on top plus left parenthesis negative 1 minus 1 right parenthesis straight j with hat on top plus left parenthesis 2 minus 1 right parenthesis straight k with hat on top equals straight i with hat on top minus 2 straight j with hat on top plus straight k with hat on top 

Now, area of triangle PQR = 1 half open vertical bar stack P Q with rightwards harpoon with barb upwards on top cross times stack P R with rightwards harpoon with barb upwards on top close vertical bar space

PQ with rightwards harpoon with barb upwards on top space cross times stack P R with rightwards harpoon with barb upwards on top space equals space open vertical bar table row i j k row 1 1 1 row 1 cell negative 2 end cell 1 end table close vertical bar space equals space 3 i with hat on top space minus space 3 k with hat on top space space space space a n d

open vertical bar stack P Q with rightwards harpoon with barb upwards on top space cross times stack P R with rightwards harpoon with barb upwards on top close vertical bar space equals space square root of left parenthesis 3 right parenthesis squared minus open parentheses 3 close parentheses squared end root space equals space 3 square root of 2 space 

Therefore, area of increment PQR comma space=1 half cross times 3 square root of 2 space equals space fraction numerator 3 over denominator square root of 2 end fraction u n i t s 

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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.
865 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

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 is a scalar quantity?

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