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

section formula let P and Q be and it
two given points whose position vector R
o P and Q P denoted by vector a and
vector B now let us mark a point R on
the line segment PQ such that it divides
P Q into ratio M is 2n internally or
externally let us first discuss the
internal division case R divides PQ
internally in the ratio M is to n so we
can write it as fraction PR by r2 is
equal to M by N or NPR vector is equal
to M RQ vector where m and n are
positive scalars from triangles
o PR and o RQ we can write P R vector is
equal to our vector minus a vector and
RQ vector is equal to P vector minus R
vector
and we have a relation and PR is equal
to m RQ between them so we can write n
into vector R minus a is equal to M into
vector P minus R on simplifying and
finding our vector we will get our
vector is equal to and the vector plus
and a vector by M plus n hence the
position vector of the points are
dividing PQ internally in the ratio M is
2 n is given by 4 our vector is equal to
our vector which is equal to M times B
vector plus M times a vector divided by
some of the ratios M plus n let are
divides the line segment PQ externally
which means point R does not lie between
PQ point R lies on the line PQ extended
further such that PR by QR is equal to M
by N or we can write and PR vector is
equal to M Q R vector
now from triangles opq and oqr we can
write P our vector is equal to our
vector minus a vector and Q our vector
is equal to our vector minus B vector
substituting in relation and times P our
vector is equal to M times Q R we will
get n times vector R minus a is equal to
M times vector R minus B on simplifying
we will get our vector is equal to M V
minus and a by M minus n in this way we
can find out the position vector of
point our dividing line segment PQ in a
given ratio M is 2 n internally or
externally if our divides line segment
PQ in two equal halves then the vector R
is given by vector A plus vector P by 2