 Hello and welcome to the session. In this session we are going to discuss subtraction of two vectors component wise as well as we illustrate the subtraction of vectors graphically. First of all we shall discuss subtraction of vectors what is vector A minus vector B. We think of this as vector A plus or minus of vector B then we ask what minus of vector B might mean this will be a vector equal in magnitude to vector B but in the reverse direction suppose this is vector A and this is vector B. Now we will draw minus of vector B whose magnitude is same as of vector B but it is in opposite direction to vector B. Now this is minus of vector B. Now we see that subtracting vectors A and B is same as adding minus of vector B to vector A that is vector A minus vector B is equal to vector A plus of minus of vector B. Now this is vector A and this is vector B. Let us draw vector B in opposite direction with same magnitude. Now this is minus of vector B. Now let us join initial point of vector A and terminal point of vector B by triangle addition this is resultant vector that is vector A plus of minus of vector B which is equal to vector A minus vector B. Thus we see that minus of vector B is additive inverse of vector B with same magnitude but in opposite direction. We should note that when we draw negative of a given vector then negative of a vector is either drawn parallel to the given vector or their initial points coincide such that they both lie on same line but in opposite direction. Now we shall discuss vector subtraction component wise. Suppose we have vector A which is equal to the ordered pair 3 1 and vector B which is equal to the ordered pair 2 minus 4. We will find vector A minus vector B and will illustrate it graphically. So first we shall find minus of vector B for this we multiply each component of vector B by minus 1 so we have minus of vector B is equal to the ordered pair 2 into minus 1 minus 4 into minus 1 which is equal to the ordered pair minus 2 4. So minus of vector B is given by the ordered pair minus 2 4. Now we find vector A minus vector B which can be written as vector A plus of minus of vector B. Now this is equal to vector A is given by the ordered pair 3 1 plus now minus of vector B is given by the ordered pair minus 2 4. So this is equal to the ordered pair 3 minus 2 1 plus 4 and this is equal to the ordered pair 1 5. So vector A minus vector B is given by the ordered pair 1 5. Now let us represent it graphically. First we draw vector A which is given by the ordered pair 3 1 so with any initial point we move three units to right and one unit up and we reach this terminal point this is vector A similarly vector B is given by the ordered pair 2 minus 4. So again with any initial point we move two units right and four units down 1 2 3 4 and we reach this terminal point here we have negative y component thus vector B is in downward direction now minus of vector B is given by the ordered pair minus 2 4. Now we draw minus of vector B at the terminal point of vector A so treating terminal point of vector A as initial point of minus of vector B we move two units to left as there is negative x component and then four units up that is 1 2 3 4 and we reach this point now this is minus of vector B we see that minus of vector B is parallel to vector B and is equal to its magnitude but in opposite direction now we join initial point of vector A and terminal point of minus of vector B and their resultant is vector A minus vector B see from initial point of vector A we moved one unit right and one two three four five five units up so components of resultant vector A minus vector B are given by one five which is same as we have calculated earlier thus in this session we have learned subtraction of two vectors component wise graphically this completes our session hope you enjoyed this session