It is the study of one object with respect to other. Done, okay.
Let’s consider two objects A and B, they are moving in, they are moving in 3D, they are moving in any direction. Like two birds, one is flying here, one there, random, anywhere. Now suppose at any time A object is here and at that time B object is here, okay. Tell me something, what is this, what is that, this vector? Position vector of A with respect to origin, that means according to origin, this must be the position vector of A with respect to O, O the origin. And what do you think of this one?
[students answering]
Definitely position vector of B with respect to origin. See, I am writing position of A with respect to origin, position of B with respect to origin. Certainly I can write position of B with respect to A. What should be the vector? Vector joining from A to B. Yes or no? So this becomes position vector of B with respect to A. Now see, the velocity of A that will be responsible to change the position of this vector. Because of the velocity of A, the position of rAo will change or no? And because of the velocity of B, rBo will change. What will be the cause of this changing?
[Students answering – both]
Both. Meaning relative velocity of B with respect to A.
Now look carefully, if I use the triangle approach, then you can see that out of the three vectors one vector is resultant.
[yes, sir]
Which one is resultant? rBo. How do you get that? Two head and two tail, you can write it like this. Okay? That means I get a new formula. Position vector of B with respect to A is written like write the position vector of B with respect to O and A with respect to O and then you minus that. Done? This is simple.
See generally we discuss motion by using the parameters given with respect to ground. So I am rewriting the concept by using reference as ground. So position vector of B with respect to A is position vector of B with respect to ground meaning real position vector minus real position vector of A. Meaning position vector of A with respect to ground. Okay?
This will change, this will change, so this also will change. Just differentiate it once. What will happen if you differentiate it once. What is dr by dt, velocity vector. So if you will differentiate this function once you will get okay, so I will get the famous formula of velocity vector. Relative velocity of B with respect to A is the……