 Myself, Mr. A. N. Suvade, Assistant Professor, Department of Mechanical Engineering, Valchand Institute of Technology, Solaapur. Today, we are going to learn relative velocity in a mechanism. Learning outcome, at the end of this lecture, students will be able to use the applications of vectors in identifying the relative velocity of a link. So, consider body A and body B. Both are moving in a straight line with velocity V A and V B, where velocity of point A is greater than velocity of B. Now, the relative velocity of A with respect to B or B with respect to A that can be determined by drawing the vector diagram. So, as we know, the velocity of point A is V A as shown in the figure. So, from fixed point O, draw a vector O A. This vector O A represents the velocity of point A in magnitude as well as in direction. Similarly, the velocity of point B is given by V B in magnitude and direction as shown in the figure. So, from point O, draw a vector O B, which will represent the velocity of point B, which is represented by V B. And now, if you want to find out the relative velocity of point A with respect to B, then velocity of A with respect to B is nothing, but it is the vector difference of V A and V B, vector difference of V A and V B and that is equal to V A minus V B. So, relative velocity of A with respect to B, it is shown by vector B to A. So, relative velocity of A with respect to B that is represented by vector B to A. And therefore, in the form of vector, the relative velocity of A with respect to B is represented by vector B A, which is equal to vector difference of V A and V B. So, velocity of A represented by vector O A minus vector O B. This is my equation number 1. Similarly, if we find out the velocity of B with respect to A, then it is equal to vector difference of V B and V A. So, in the vector diagram, the velocity of B with respect to A, it is represented by vector A to B. So, this vector A to B that will represent the velocity of B with respect to A. So, this is the velocity of B with respect to A. And now, velocity of B with respect to A, it is represented by vector A B that is equal to vector difference V B minus V A and that is equal to vector A B is equal to velocity of B is represented by vector O B minus O A. This is my equation number 2. So, here the relative velocity of A with respect to B and B with respect to A is determined. And hence, from equation 1 and 2, we can conclude that velocity of A with respect to B and velocity of B with respect to A. Both are equal in magnitude, but they are opposite in direction. Similarly, when the one of the body is moving in a straight line and other body is moving in an inclined path. So, body A is moving with velocity V A in a horizontal direction as shown in the figure and body B is moving in an inclined direction. So, in this case, the relative velocity of A with respect to B or velocity of B with respect to A, it is determined by drawing a velocity triangle diagram. So, for that, we will use the law of velocity triangles. So, let us first of all draw the velocity diagram. So, for drawing the velocity diagram, first of all mark point O in space. And from point O, draw a vector O A, which will represent the magnitude and direction of body A. And similarly, from fixed point O, draw a vector parallel to V B, which will represent the magnitude and direction of body A. So, this vector O B represents the velocity of B. And now, if you join the vector B A, this vector B A, it will represent the relative velocity of A with respect to B. And therefore, from this triangle, we can also determine the relative velocity of A with respect to B or B with respect to A. And hence, from the velocity triangle, V of A B, relative velocity of A with respect to B is equal to vector difference of V A and V B. And therefore, velocity of A with respect to B is represented by vector B A, which is equal to V A minus V B. So, V A is represented by vector O A and V B is represented by vector O B. So, this is my equation number 3. Similarly, if I want to find out the relative velocity of B with respect to A, then V B A is equal to vector difference of V B minus V A. So, that will be equal to vector A B is equal to velocity of B minus V A. So, V A is represented by vector O B minus vector O A. So, this is my equation number 4. So, from equation 3 and equation 4, what we can conclude? So, my dear student, please think the equation number 3 and equation number 4, what you can interpret from these equations. So, from equation 3 and equation 4, we can interpret that velocity of A with respect to B or velocity of B with respect to A, both are equal in magnitude, but they are opposite in directions. So, this particular material is referred from a book of theory of machines by Aryas Khurmi and theory of machines by S.S. Vatan. Thank you.