Examples : Section Formula Video Lecture | Mathematics (Maths) Class 12 - JEE

hello friends this video on vector
algebra part 15 is brought you by exam
create calm no more fear from exam
before watching this video please make
sure that you can watch part 1 to part
14 let's take for example the section
formula the question says the position
vector of a point are you refine which
divides line joining two points P and Q
in 2 is to 1 so let's draw what the
question is trying to say I have two
points I have one point P here and I
have one point Q later and let's suppose
this is my origin right so I have my B
vector I have my cute
then let's suppose this is my point
right now the question is saying that
there's a line the giant speed to Q so
it is P to chew it is not Q to be
pleased now it speed to chew this is my
life the question says there is a vector
R this is my vector R this guy divides
this rich line 2 is to 1 so this is 2
this is 1 correct please note I should
not take 2 is to 1 like this why because
from P to Q it divides 2 is to 1 if you
take in this fashion 2 is to 1 you will
get a wrong answer that logically is not
the question what is not what the
question is asking for please pay
attention here you have two vectors P
and Q and there is a again our vector
the joints there is 2 point P in Q is
the vector that joins P to Q and then
there is a point R the vector R actually
which divides this line 2 is to 1 since
you are going from P to Q you should
take to this to 1 like this not like
this please note 2 is to 1 has to be
this not 1 is true this guy is 1 is to 2
this is raise to H to 1 you are going
from P to Q so you take always this
fashion correct so so let us suppose it
is
M into n actually so in this fashion if
you assume this guy is M and this base
and let's say correct so if this guy's M
this guy has to be e and this guy has to
be if you assume that way then our
vector actually is nothing but M into
opposite vector that is M into a vector
plus n into first vector this B vector
divided by and Plus don't need confuse
here the formulas always in this fashion
this value or against a M into a
positive factor plus this guy whatever
value we have here into a positive actor
/ intercept so in this case it will be M
is to a right this is real correct M is
2 into a vector normal is this guy's a
record here nothing but Q vector and Q
vector was mine this guy minus I 2 plus
J plus K minus I plus J plus K plus N
and there is 1 into B vector this P
vectors position vector of P that is
this guy I plus 2 J minus K by M plus n
that is 1 M is 2 n is 1 this is nothing
but minus 2 plus 1 what is minus 1 minus
I plus 2 J plus 2 J plus 4 C correct 2k
minus k plus K right whole thing divided
by 3 and this is nothing but minus I by
3 plus 1 by 3 e j+
and that is masked Naga difficult the
only trick here is please understand
that if it is two years to one you
should take two hair one this side
because I am going from P to Q and then
you just name a and B here anything then
you say two into a positive vector plus
1/2 plus the vector let's say the same
version and in this case it divides
externally so again I have one P and I
have one my Q let this be your ISM right
so this is the case and there is some
external point R here so I am going from
here to here
East region then I am going to this this
external point here huh so I am saying
this guy is to here from here to here
because it is 2 is to 1 and from here to
here is one correct that's what it says
correct so let me assume here also let
me assume this guy's a and this guy's B
so here also I will say 2 into opposite
vector so in this case this will be this
guy B so my R vector will be M because
this is M this guy is n is M and this
guy's alien suppose M into a buzz vector
B item - space m n into a vector by M -
let us put the value M is 2 B vector
here is this way that is this thing
because this guy is Q right Q is be
there is minus I plus J plus K minus n
is 1 a vector a vector is nothing but my
P
that is I plus 2j minus k whole thing
divided by M minus and there is two
minus one that is one cool thing is
divided by 1 so this becomes 2 into
minus 1 is minus 2 minus 1 is minus 3
minus 3 I plus 2 J minus 2 J is 0 Z plus
2 K minus K is kill it sorry 3 K 2 K
minus minus plus so 2 k plus K 3 K this
is nothing but minus 3i plus and that is
nice
so you see you get different answers in
both cases in one case it was internal
division the other gilworth
externalization the cash hell you have
to actually find out it is 2 is to 1
that means you start from where you
start from here P is 2 R will be 2 and
then R is 2 P will be 1 2 is to 1 and
then to get the formula M into above
this side this will be minus n intervals
side by M minus M find the position
vector of the midpoint of the vector
joining this point and this one so I
have two points P and Q here again this
might feel in this manner I have to find
the vector joining midpoint of this that
it is dividing into one to one ratio and
I have to find this already the internal
division so our vector will be nothing
but if you assume this guy as a vector
this B vector 1 into e vector last
morning to be vector by 1 plus 1 that is
a vector plus D etre title so a vector
is P vector and B 8 rescue vector so
let's do this character is this guy P
etter
that is 2i plus 3 J plus 4 K right plus
B vector is this guy
for I plus 1 J minus 2 K respecter
divided by 2 2 plus 4 s 6 6 I 3 plus 1
is 4 4 J 4 minus 2 is 2 plus 2 divided
by D this is nothing but 3 I plus 2 J
plus key and that is mines just use the
section form line cut them as thank you
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