Find the angle between given vector with the help of given angle. Not visible. Ok I will redraw the figure for you. Three vectors, we need to find angle between PQ, QR and PR. If I have given you some example 45, 45 and this angle 90 deg.

Tell me what is the angle between P and Q? What is the angle between Q and R?

What is the angle between R and P? Vector.

We have a rule to find the angle between two vectors and one information given.

What is the information? And information is you can shift the vector parallel to itself; it is not going to change. Now shift vector parallel to parallel and join tail to tail.

If I want to work out the angle between two vectors then I have shift both vectors and any one vector in such a manner that is join tail to tail. After joining tail to tail, smaller angle will be termed as angle between two vectors. So what will be angle in this particular scenario? Let us work out this problem.

Say if I want to find angle between P and Q then shift any one vector. We will do one thing we will shift P vector. Can I shift P vector parallel to itself?  Yes and if I shift P vector parallel to itself, it will come in this particular place. now P and Q are in a state of tail to tail. Then this angle will define angle between segments. Isn’t it? What is that angle, 90 degrees? Done.

So angle between P vector and Q vector is 90 degrees. First answer.

Let us talk angle between Q and R. So shift Q or R, whichever you like which is easier. I feel if I shift Q upwards then it meets tail of R. see I am shifting R like this. Now they have joined tail to tail. Now tell me what is the angle?  This angle will be between Q and R vector .Angle between two vectors will be anything between 0 to 180 degrees. So 135 is the angle. Done

Now angle between P and R.