in this video we will talk about vector
addition and Vector subtraction now to
understand the addition of two vectors
let us consider two vectors A and B that
lie in the same plane or I shall say
that both these vectors A and B are
c-liner as can be seen in this figure
now you must note that here the lengths
of the line segment representing these
vectors are proportional to the
magnitude of the vectors now to find the
sum of these two vectors you would have
to place vector B so that its tail is at
head of vector a as shown in this figure
after this join the tail of vector a to
the head of vector b as can be seen from
the figure this line o q represent
Vector C which is equal to the sum of
both vectors A and B so here we have
Vector C = A + B this procedure of
vector addition where two vectors and
their resultant from three sides of a
triangle is known as triangle method of
vector addition let us learn more about
vector addition now vector addition is
commutative that is if we find the
resultant of b + a then we obtain the
same resultant Vector that is C so here
we have a + b isal to B + a another
property of vector addition is that it
is associative that is the result of
adding vectors A and B first and then
adding Vector C is same as the result of
adding Vector B and C first and then
adding Vector a now consider two equal
and opposite vectors A and minus a as
shown in this figure now if we add these
two equal and opposite vectors their sum
would be equal to zero that
is
A+ minus
a is equals to
a -
A which is equals to0 this is because
the magnitude of these two vectors are
same but they have opposite directions
and the resultant Vector has zero
magnitude and is known
as null
Vector since null Vector has zero
magnitude we cannot specify its
direction now I would like to State one
more point about vector addition that is
when it comes to add vectors
representing phys physical quantities
like displacement here while drawing
diagram for addition of displacement
vectors you are not required to draw
vectors to their actual size it is often
convenient to use a scale in which the
distance on diagram is proportional to
the actual size for example in vectors
you can use 1 cm to represent 10 km just
as you do on the map you can use such
scales with other Vector quantities for
example in case of four you might to use
a scale in which 1 cm long Vector
represents a force of 5 Newton Now we
move on to subtraction of vectors
subtraction of two vectors can be
defined in terms of addition of vector
for this consider a case when we
multiply a vector uh say a by Min -1 so
-1 into a = to Min - A and this minus a
is by definition of vector that have the
same magnitude as Vector a but have
opposite direction so here the
difference of two vectors A minus B can
be defined in terms of sum of two
vectors A and minus B that is a - b is =
to a + minus B and we can use triangle
or polygon method of vector addition to
get our answers to understand
subtraction of two vectors let us
consider two vectors A and B as shown in
this figure now this figure also shows a
vector Min - B where Min - B is = to -1
B so as we stated earlier difference of
two vectors A and B would be equal to
the sum of two vectors A and minus B now
to obtain the difference we would Place
Vector minus B in such a way that its
tail is at head of vector a so this
figure shows both addition and sub
subtraction of vectors A and B for the
purpose of comparison here Vector R2 is
equal to a minus B which is the
difference between two vectors A and B
and Vector
R1 is equal to a + b which is the
addition of two vectors A and B next
thing I want to talk about in this video
is parallelogram method of vector
addition again to understand this method
of vector addition let us consider two
vectors A and B now to add vectors using
this method place the tail of vector B
so that it meets the tail of vector a as
shown in this figure in the next step
take these two vectors to be the first
two adjacent side of a
parallelogram and now draw the remaining
two sides in this figure dotted line
shows remaining two sides of the
parallelogram now to get the sum of
vectors A and B draw a vector that
extends from the tail of vector A and B
across the diagonal to the opposite
Corin of the parallelogram now in this
figure Vector o r shows the sum of
vectors A and B so
this o r is = to
R = to a + b sometimes it is common
error to draw some vectors as diagonal
running between tips of two Vector for
example vector Vector q p in this figure
this is incorrect it does not represent
the sum of two Vector in fact it
represent the difference that is a minus
B so we can use both triangle method and
parallelogram method to add vectors now
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