Position Vector - Vector Algebra, Math, Class 12 Video Lecture

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what is position vector
oh this ship occurrence if you have any
point in the space so let's suppose you
have any point in the space P with some
coordinates X Y Z and you draw a line
from origin and add to the P you get
positioning example you have this XYZ
coordinates T first thing we do is we'll
check if it is right hand currents
terminar so from eggs
there is eggs will mold are four fingers
to Y right in this section and we will
see that Z should point to so I thumb
should point to Z and here my thumb will
point to Z right ooh a small test and we
see our system is correct now what I can
do is you take any point p on the space
and let this horrid V X Y Z this is my
some point and I have to find the
position electrons do those you have
this origin you join this you join this
this guy became the position rating
please note this guy whole thing is
positioning right at magnitude opa and
the value of papi mod will be root of X
square plus y square plus Z square this
we can very easily prove from Pythagoras
theorem also how if you see this and do
that
I will take a better view of this in 3d
n let's draw this kind of diagram so
it's a 3d view of the same thing
actually then you can visualize things
better so you see here I have to prove
that my R vector is my R vector Ashley
the magnitude of this there is Opie
length of Obi's X square plus y square
plus X square where my as I told that
this point is x y&z correct so that
means if you take this point and draw
this line here right and from here to
here in the X direction this will become
length X similarly this guy is y so if
you draw from here perpendicular to y
direction right this guy is y and
similarly from here if you draw a
perpendicular direction this side right
this length will be z correct noise it
will know so what we can do is you can
see that this guy our this guy is right
triangle actually if you see our is
nothing but my x squared plus ap square
correct so let me say R is nothing but
root of in this triangle X square plus Z
square in triangle a oh my yo P is a
right triangle correct a o P is a right
triangle and where this triangle is
right why triangle so my R is nothing
but root of X square plus this guy way
because you see my FB is like this sorry
a is here he is here my OB is our AP is
something which we do not find and O is
X so we can say that R is X square plus
ap square root what is ap square AP is
nothing but if you see ap in this
triangle this particular triangle
you see this triangle as II the L at
this point B M and right so ap square is
P n square plus n square P n is Z and NP
is y so ap is nothing but root of X
square plus first or a P Square is going
to expand plus y square so instead of AP
square I will say sorry Y square plus
del square Y is X square plus y square
so ap square is y square this is so what
do you get R is nothing but root of X
square plus y square listen and that's
what I have written
correct magnitude of R this is my R
vector o P is my R vector and the
magnitude of this R vector is X square
plus y square plus X and it will be
using this formula very often so please
remember this you have some position
vector P with some point XYZ then the
distance of that point from origin o is
root of X square plus y square plus Z
square how we got this by applying
Pythagoras theorem twice we had this
triangle a opie in this triangle this
angle is 90 degree so we told that this
this length is magnitude of R is equal
to root of X square plus ap square this
formula the same thing I write wrote a
piece where s Y square plus Z square
because AP is nothing but root of Y
square plus that's thus I got magnitude
of a position vector or this of the
position vector from origin is X square
plus y square plus Z square where X Y Z
or its contents so I hope you understood
this that we have this coordinate system
we verified that this particular
coordinate system is the right hand
corner
system we are looking for and then we
had some point P some point period with
XYZ is coordinates we found the position
vector of that will I'll tell you how to
write this guy also this guy I can write
as X I plus YJ plus ZK and tell you how
to do this this is a vector
representation of this P right P vector
is nothing but this here saying our R
vector actually
so R vector is X I plus y J plus ZK
where if you see in I direction I
direction this X is I direction the
length was X in y direction the capital
y direction the length was y so it is y
IJ in capital Z direction the length was
small Z so it is small that character
because this vector is a vector this guy
Y is Z J vector and this Z is give it
this is the convention we use I J and K
will tell you how to do this and that's
how we write this so I can write this R
vector as X I plus y G Plus Z K also
correct and the magnitude of this R
vector magnitude will be nothing but you
go X square plus 1 square please thank
you
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