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Physics Part I

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Resolve the rectangular components of a vector in three dimensions?

Let us resolve the rectangular components of a vector straight R with rightwards arrow on top represented by <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre> in three dimensions.

                

From point P, draw a perpendicular PM on XY plane and from M draw a perpendicular PM on XY plane and from M draw perpendicular ML on Y axis and MK on X axis. '

Using triangle law to increment OKM comma

OM with rightwards harpoon with barb upwards on top space equals space OK with rightwards harpoon with barb upwards on top space plus KM with rightwards harpoon with barb upwards on top space space space space space space space space space... thin space left parenthesis 1 right parenthesis

Using space triangle space law space to space increment OMP comma

OP with rightwards harpoon with barb upwards on top space equals space OM with rightwards harpoon with barb upwards on top space plus space MP with rightwards harpoon with barb upwards on top space space space space space space space space space space space... space left parenthesis 2 right parenthesis space

From space equation space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space

stack OP space with rightwards harpoon with barb upwards on top space equals space OK with rightwards harpoon with barb upwards on top space plus KM with rightwards harpoon with barb upwards on top space space plus MP with rightwards harpoon with barb upwards on top

Here comma space vector space OK with rightwards harpoon with barb upwards on top space comma space KM with rightwards harpoon with barb upwards on top space and space MP with rightwards harpoon with barb upwards on top space are space mutually
space perpendicular space to space each space other. space Therefore comma space
vectors space OK with rightwards harpoon with barb upwards on top space comma space KM with rightwards harpoon with barb upwards on top space and space MP with rightwards harpoon with barb upwards on top space are space called space rectangular
space components space of space vector space straight R with rightwards harpoon with barb upwards on top. space

Now comma space straight X comma space straight Y space and space straight Z space components space are space represented space
by space straight R with rightwards harpoon with barb upwards on top subscript straight x comma space straight R with rightwards harpoon with barb upwards on top subscript straight y space and space straight R with rightwards harpoon with barb upwards on top subscript straight z space respectively.

Unit space vectors space along space straight X comma space straight Y space and space straight Z space axis space are space straight i with hat on top comma space straight j with hat on top space and space straight k with hat on top.

So comma space resultant space is space given space by comma space

straight R with rightwards harpoon with barb upwards on top space equals space stack straight R subscript straight x with rightwards harpoon with barb upwards on top space plus space stack straight R subscript straight y with rightwards harpoon with barb upwards on top space plus space space stack straight R subscript straight z with rightwards harpoon with barb upwards on top
space
If space vector space straight R with rightwards harpoon with barb upwards on top space space has space magnitude space straight R space and space makes
angle space straight theta subscript straight x comma space straight theta subscript straight y space and space straight theta subscript straight z comma space with space positive space direction space
of space straight X comma space straight Y space and space straight Z space axis space respectively comma space then

OK space equals space straight R subscript straight x space equals space straight R space space cos space straight theta subscript straight x
KM space equals space straight R subscript straight y space equals space straight R space sin space space straight theta subscript straight y
MP space equals space space straight R subscript straight z space equals space straight R space sin space space straight theta subscript straight z

Thus comma space straight R with rightwards harpoon with barb upwards on top space equals space straight R subscript straight x straight i with hat on top space plus space straight R subscript straight y straight j with hat on top space plus space straight R subscript straight z straight k with hat on top

space space space space space space space space equals space space space Rcos space straight theta subscript straight x space straight i with hat on top plus straight R space sin space space straight theta subscript straight y straight j with hat on top space plus straight R space sin space space straight theta subscript straight z straight k with hat on top

The above expression gives us the rectangular components of a vector in three dimension. 
               

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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.
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

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

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views