 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that, find the magnitude and direction of vector AB whose initial point A is at 11 and terminal point B is at 65. We know that the component of vector AB whose initial and terminal points are A with coordinates x1, y1 and B with coordinates x2, y2 is given by the ordered pair x2 minus x1, y2 minus y1. Its magnitude is given by the formula square root of x2 minus x1 whole square plus y2 minus y1 whole square and its direction is given by tan of theta is equal to y2 minus y1 the whole whole upon x2 minus x1. With this key idea, we shall proceed to the solution. In this question, we have to find the magnitude and direction of vector AB whose initial and terminal points are given. Using formula of magnitude given in key idea, we find the magnitude of vector AB. Now, magnitude of vector AB is equal to square root of x2 minus x1 whole square plus y2 minus y1 whole square. So, this is equal to, now x2 minus x1 will be given by 6 minus 1 whole square plus y2 minus y1 that is 5 minus 1 whole square. That is, here we have taken x1, y1 as 1, 1 and x2, y2 as 6, 5 and this is equal to square root of 6 minus 1 that is 5 square plus 5 minus 1 that is 4 square which is equal to square root of 25 plus 16 which is equal to square root of 41 which is approximately equal to 6.4. So, we say that magnitude of vector AB is about 6.4. Now, we shall find direction of vector AB. From this key idea, we know that direction is given by tan of theta is equal to y2 minus y1 the whole whole upon x2 minus x1. To find direction of vector AB, we know that it is given by the formula tan of theta is equal to y2 minus y1 the whole whole upon x2 minus x1 and here the coordinates of initial point and terminal point are given. So, we substitute these values in the formula which implies that tan of theta is equal to y2 minus y1 that is 5 minus 1 whole upon x2 minus x1 that is 6 minus 1. So this implies that tan of theta is equal to 4 by 5. Now, taking its inverse we get theta is equal to tan inverse of 4 by 5. Now, using calculator we get the value of tan inverse of 4 by 5 as 38.65 degrees approximately. Thus vector AB has a direction of about 38.65 degrees which is the required answer. This completes our session. Hope you enjoyed this session.