Examples : Part 2 - Introduction to Three Dimensional Geometry Video Lecture - Mathematics (Maths) Class 11 - Commerce

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have watched part 1 to part 4 in this
example we have to find the coordinates
in the centroid will triangle is what is
our x1 y1 z1 x2 y2 z2 and x3 y3 z3 so
what we are given we are given that
there is a triangle here this is x1 y1
z1 x2 y2 z2 and this is x3 y3 z3 right
there suppose this point is p1 this is
p2 this is P we have to find centroid to
find sign point first you have to find
the midpoint of this and then we have to
divide at that point in to which to one
ratio all right so let's suppose this
point is Q and this point is our R is
the centroid
so first let's find the value of point Q
correct so Q will be P 1 plus P 2 by 2
because it is a midpoint here so Q will
nothing mean but X 1 plus X 2 by 2 comma
Y 1 plus y 2 by 2 comma Z 1 plus Z 2 by
this is the value of point Q correct now
we have this point Q and we have this
point P 3 now P 3 and Q both divides
into 2 is to 1 ratio now you to find the
value of r r will come out to be 2 into
Q I'll say R is nothing but 2q plus P by
2 plus 1 correct that is the image to
animilitia
so they'll say 2 into Q always that is 2
into X 1 plus X 2 by 2 plus T 3 that is
X 3 by 2 plus 1
similarly this will be 2 into y 1 plus y
2 by 2 plus y 3 by 3 comma 2 into Z 1
plus Z 2 by 2 plus Z 3 by correct this
by 2 by 2 cancels bye - bye - ensign bye
- bye - bye sir
so what we got our is nothing but X 1
plus X 2 plus X 3 by 3 comma y 1 plus y
2 plus y 3 by 3 is 3 comma Z 1 plus Z 2
plus Z 3 by this is the value a apart so
if you want to find the centroid of the
triangle that is X 1 plus X 2 plus X 3
by 3 y 1 plus y 2 plus y 3 by 3 3 by 3
we have XY X 1 y 1 then 1 X 2 y 2 Z 2 X
3 by 3 3 all these are coordinates on
the points of the triangle what we have
done we have just found point Q there is
a midpoint of P 1 and P 2 and then we
are bound for the point R that is this
is divided the line PQ in 2 is to 1
ratio will take for example we have to
find the ratio in which the line segment
joining 4 8 10 and 6 10 minus 8 is
divided by why is that a plane it is
something like this we have this point I
suppose this P this is Q so we have
point P and Q and then there is a line
that is why is that plain why is that
plain this divides this be queuing in
let's suppose K store direction you have
to find the cage to one ratio actually
so if it is wise that plane we can say
that X will be 0 correct because in case
our Y Z plane x value 0 so let's find
the x coordinate in this case so this is
hole 8 10 and this is 6 10 - and let's
suppose this point is o so our X that is
X off point are there is nothing but K
into 6
k into 6 plus 4 into 1 by k plus 1 and
this dial is equal to 0 we are told
correct
so we get 6 k plus 4 is going to 0 or he
is equal to minus 2 by 3 st. is minus 2
by 3 then we can say that this ratio is
2 by 3 and this is externally correct
what we have done very simple we have
got this point and we know that X in Y Z
plane X equal to 0 here we have to find
the coordinate of the point which
trisect the line so I need P and Q where
P is 4 2 minus X and Q is 10 minus 16
and 6 let's see what we are trying to
say here let's draw the line first so
let's suppose this is our line this is
the point B and it is the point Q now we
are saying it twice X that means it is
three equal parts and let's suppose this
is point a and this point is B me and we
have to find the value of a and B where
P point is given that is 4 2 minus 6 and
Q point is given that is 10 minus 16 and
6 we have to find a and B now since
these are all equal part this is all
equal part so we can say that a divides
in ratio 1 is to do correct because this
is one part this is two part also we can
say that B divides into each to one
ratio because this part is to end this
part is 1 so what do you have to do we
have to just find the value of a and B
we know the ratio at which this point
divides P and Q so we can say that a is
nothing but so this a ax is nothing but
10 into 1 plus 2 into 4 by 2 plus 1
correct and that comes out to be 10 plus
in a 18 by 3 that is 6 this ax
similarly a Y comes out to be 1 into
minus 16 plus 2 into 2 by 2 plus 1 and
that value is nothing but minus 16 plus
4 is minus 12 by 3 is minus 4
similarly easy turns out to be 1 into 6
plus 2 into minus 6 by 2 plus 1 and that
value comes out to be 6 minus 12 is
minus 6 by 3 is minus 2 so we know that
a point is nothing but 6 minus 4 and
minus 2
similarly point B if you have to find B
is nothing but because this is in the 2
is to 1 ratio so this will be 2 into 10
plus 1 into 4 by 2 plus 1 this point
will be 2 into minus 16 plus 1 into 12
by 2 plus 1 and this point will be 2
into 6 plus minus 1 into 6 right by 2
plus correct so this value comes out to
be 4 plus 12 16 plus 20 is 20 4 by 3
that is 8 this is minus 32 plus 12 that
is - strain - 32 plus 12 that is minus
20 by 3 correct this is this is the
minus 6 32 plus 2 because this is wine
to do that is minus 30 by 3 that is
minus 10 and this is 12 minus 6 is 6 by
3 that is so v-point is nothing but 8
minus 10 and so we have to find
according to the point which slicing
this line so the coordinates are nothing
but a and B where AR is 6 minus 4 and
minus 2 and this is a
and B is equal to 8 minus 10 and that is
answer so what we have done we have just
plotted this point P and Q and we have
found a point a and B a and all these
are equal so a divide this line into 1
by 2 ratio and be revised design into
evolution and then we have used this
formula to get the value of a and B
thank you
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