 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that if vector U is equal to the ordered pair minus 2 1 and vector V is equal to the ordered pair 4 3 sketch its resultant using parallelogram rule and find vector U plus vector V. We know that in parallelogram rule of addition if vector U is equal to the ordered pair x1 y1 and vector V is equal to the ordered pair x2 y2 then the resultant vector is given by sum of the two vectors that is vector U plus vector V that is equal to the ordered pair x1 plus x2 y1 plus y2. With this key idea we shall proceed to the solution we are given vector U which is equal to the ordered pair minus 2 1 and vector V which is equal to the ordered pair 4 3. Let us first draw these two vectors since we have to use parallelogram rule so we draw these vectors on plane having same initial points now here we take this point as initial point and we know that vector U is given by the ordered pair minus 2 1 so we move two units left and one unit up to reach terminal point of vector U in upward direction this is vector U and vector V is equal to the ordered pair 4 3 so with same initial point we move four units right and three units up to reach terminal point of vector V with upward direction so here we move four units to right that is one two three four and three units up that is one two three so this is the terminal point of vector V and this represents vector V now we complete this parallelogram we draw dotted line parallel to vector U at terminal point of vector V and similarly we draw dotted line parallel to vector V at terminal point of vector U this is the required parallelogram draw resultant vector by joining the initial point of the two vectors with the opposite vertex of the parallelogram this vertex is the terminal point of the resultant vector and is also in upward direction let us name this resultant vector as R and this resultant vector is equal to vector U plus vector V that is resultant vector R is equal to vector U plus vector V we can find the components of the resultant vector by using the key idea so here vector U is equal to the ordered pair minus 2 1 and vector V is equal to the ordered pair 4 3 so resultant vector R which is equal to vector U plus vector V will be equal to ordered pair minus 2 1 plus ordered pair 4 3 which is equal to the ordered pair minus 2 plus 4 1 plus 3 that is equal to the ordered pair 2 4 if we see in this figure from initial point we moved two units right and 1 2 3 4 4 units up to reach terminal point of resultant vector so its components are given by the ordered pair 2 4 thus vector U plus vector V is given by the ordered pair 2 4 which is the required answer this completes our session hope you enjoyed this session