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Motion in A Plane

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Physics Part I

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Physics

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Class 10 Class 12

Two vectors straight A with rightwards arrow on top space and space straight B with rightwards arrow on top are represented by the two sides of a parallelogram drawn from point O. Show that the diagonal not passing through O is given by plus-or-minus left parenthesis straight A with rightwards arrow on top minus straight B with rightwards arrow on top right parenthesis.


Let two vectors straight A with rightwards arrow on top space and space straight B with rightwards arrow on top be represented by two adjacent sides of parallelogram OP and OQ drawn from O as shown in the figure. to complete the parallelogram OPSQ.



That space is comma space

OQ with rightwards harpoon with barb upwards on top space equals space straight B with rightwards harpoon with barb upwards on top space and space OP with rightwards harpoon with barb upwards on top space equals space straight A with rightwards harpoon with barb upwards on top

Through space straight O space draw space straight a space vector space OM with rightwards harpoon with barb upwards on top space equal
space and space opposite space to space space to space OQ with rightwards harpoon with barb upwards on top.

therefore space OM with rightwards harpoon with barb upwards on top space equals space minus straight B with rightwards harpoon with barb upwards on top space

OPNM space parallelogram space is space completed. space

Now comma space according space to space the space parallelogram space vector space of space addition comma space

ON with rightwards harpoon with barb upwards on top space equals space straight A with rightwards harpoon with barb upwards on top space plus space left parenthesis negative straight B with rightwards harpoon with barb upwards on top right parenthesis space equals space straight A with rightwards harpoon with barb upwards on top space minus space straight B with rightwards harpoon with barb upwards on top

Since space the space sides space of space the space parallelogram space OPSQ space and space OPNM
space are space equal space and space parallel comma space therefore comma space their space diagonals space are
space also space equal space and space parallel. space

straight i. straight e. comma space ON with rightwards harpoon with barb upwards on top space equals space QP with rightwards harpoon with barb upwards on top

therefore space ON with rightwards harpoon with barb upwards on top space equals space straight A with rightwards harpoon with barb upwards on top space minus space straight B with rightwards harpoon with barb upwards on top

and space NO with rightwards harpoon with barb upwards on top space equals space minus space left parenthesis straight A with rightwards harpoon with barb upwards on top space minus space straight B with rightwards harpoon with barb upwards on top right parenthesis

Hence comma space the space diagonals space ON with rightwards harpoon with barb upwards on top space and space NO with rightwards harpoon with barb upwards on top space not
space passing space through space straight O space represent space the space difference space of space two space vectors. space

125 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 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 scalar quantity?

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

Give three examples of vector quantities.

Force, impulse and momentum.
865 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