So far, okay, so far we have discussed the addition and subtraction of two vectors. Now let’s see one more mathematical operation which is very much important for the understanding of various aspects of physics and that is the product of two vectors. So let us discuss the product of two vectors.

Depending upon the end result the product of vectors is divided into two categories, okay. One is scalar product and the other one is the vector product. Why are they given names scalar and vector, that is very much easy to analyze? That means these kinds of products will give you a scalar result when a product of two vectors resulting into a scalar quantity, the product is known as the scalar product and when the result is a vector quantity it is a vector product. To represent them separately for scalar we use dot between two vectors, A dot B so it is also known as dot product. And to represent the vector product we use cross, A cross B so it is known as cross product, okay. So they are also known as scalar dot product and the cross product. So we will consider first the scalar product and then we will move to the vector product.

So what is the topic of today’s lecture, that is the dot product of two vectors, done.

Dot product. Dot product of vectors is defined as A dot B, A dot B, now I have put this dot, right, so that is why it is also known as the dot product. And what will be the result? Result will be a scalar quantity, it will be C and C will not be vector. So C will be a scalar quantity.

And if C is a scalar quantity it will carry only magnitude. It won’t have any direction. So what is the magnitude of C, magnitude of C is defined as A B cos theta. What is A? The magnitude of A vector. And what is B? Magnitude of B vector. And what is the theta? It is angle between A vector and B vector. And as we use the word ‘angle’ then what thought should come to mind, tail to tail. How to define the angle between two vectors? Tail to tail. So the dot product of two vectors quantities, A dot B, how do we write this, A dot B, and what will be the result? A dot B = to AB cos theta. So I have removed C from this, so what is A dot B, so it is AB cos theta. And it depends on three things, magnitude of first vector, magnitude of second vector and the angle between these two vectors.  This is how we define the dot product, that’s all.

Now we will see its application, several possible cases and several possible applications and to use it in different, different problems. Done? Any doubt? Okay. So let’s write a few cases, some important points, note down. First one….