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vector addition and subtraction
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Jun 10, 2025
In this video learn quickly about vector addition and vector subtraction
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in this video we will talk about vector
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addition and Vector subtraction now to
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understand the addition of two vectors
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let us consider two vectors A and B that
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lie in the same plane or I shall say
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that both these vectors A and B are
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c-liner as can be seen in this figure
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now you must note that here the lengths
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of the line segment representing these
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vectors are proportional to the
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magnitude of the vectors now to find the
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sum of these two vectors you would have
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to place vector B so that its tail is at
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head of vector a as shown in this figure
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after this join the tail of vector a to
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the head of vector b as can be seen from
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the figure this line o q represent
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Vector C which is equal to the sum of
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both vectors A and B so here we have
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Vector C = A + B this procedure of
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vector addition where two vectors and
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their resultant from three sides of a
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triangle is known as triangle method of
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vector addition let us learn more about
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vector addition now vector addition is
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commutative that is if we find the
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resultant of b + a then we obtain the
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same resultant Vector that is C so here
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we have a + b isal to B + a another
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property of vector addition is that it
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is associative that is the result of
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adding vectors A and B first and then
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adding Vector C is same as the result of
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adding Vector B and C first and then
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adding Vector a now consider two equal
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and opposite vectors A and minus a as
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shown in this figure now if we add these
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two equal and opposite vectors their sum
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would be equal to zero that
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is
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A+ minus
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a is equals to
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a -
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A which is equals to0 this is because
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the magnitude of these two vectors are
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same but they have opposite directions
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and the resultant Vector has zero
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magnitude and is known
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as null
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Vector since null Vector has zero
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magnitude we cannot specify its
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direction now I would like to State one
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more point about vector addition that is
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when it comes to add vectors
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representing phys physical quantities
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like displacement here while drawing
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diagram for addition of displacement
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vectors you are not required to draw
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vectors to their actual size it is often
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convenient to use a scale in which the
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distance on diagram is proportional to
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the actual size for example in vectors
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you can use 1 cm to represent 10 km just
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as you do on the map you can use such
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scales with other Vector quantities for
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example in case of four you might to use
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a scale in which 1 cm long Vector
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represents a force of 5 Newton Now we
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move on to subtraction of vectors
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subtraction of two vectors can be
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defined in terms of addition of vector
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for this consider a case when we
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multiply a vector uh say a by Min -1 so
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-1 into a = to Min - A and this minus a
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is by definition of vector that have the
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same magnitude as Vector a but have
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opposite direction so here the
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difference of two vectors A minus B can
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be defined in terms of sum of two
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vectors A and minus B that is a - b is =
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to a + minus B and we can use triangle
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or polygon method of vector addition to
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get our answers to understand
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subtraction of two vectors let us
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consider two vectors A and B as shown in
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this figure now this figure also shows a
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vector Min - B where Min - B is = to -1
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B so as we stated earlier difference of
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two vectors A and B would be equal to
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the sum of two vectors A and minus B now
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to obtain the difference we would Place
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Vector minus B in such a way that its
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tail is at head of vector a so this
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figure shows both addition and sub
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subtraction of vectors A and B for the
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purpose of comparison here Vector R2 is
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equal to a minus B which is the
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difference between two vectors A and B
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and Vector
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R1 is equal to a + b which is the
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addition of two vectors A and B next
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thing I want to talk about in this video
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is parallelogram method of vector
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addition again to understand this method
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of vector addition let us consider two
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vectors A and B now to add vectors using
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this method place the tail of vector B
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so that it meets the tail of vector a as
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shown in this figure in the next step
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take these two vectors to be the first
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two adjacent side of a
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parallelogram and now draw the remaining
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two sides in this figure dotted line
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shows remaining two sides of the
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parallelogram now to get the sum of
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vectors A and B draw a vector that
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extends from the tail of vector A and B
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across the diagonal to the opposite
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Corin of the parallelogram now in this
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figure Vector o r shows the sum of
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vectors A and B so
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this o r is = to
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R = to a + b sometimes it is common
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error to draw some vectors as diagonal
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running between tips of two Vector for
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example vector Vector q p in this figure
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this is incorrect it does not represent
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the sum of two Vector in fact it
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represent the difference that is a minus
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B so we can use both triangle method and
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parallelogram method to add vectors now
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for more notes and study material you
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can visit our website physics
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catalyst.com
#Primary & Secondary Schooling (K-12)