Let us consider a vector a. let’s say this is a vector a. Then what is the meaning of vector minus a. minus a that means a vector is multiplied by minus one. That means the vector is rotated by an angle of 180 degrees. So if a vector is multiplied by minus one that means it is rotated by an angle of 180 degrees. It’s just became opposite in direction. What happened? Just opposite. That means vector is rotated by 180 degrees. Done? Second example, say I am taking one vector b and if I am writing 2b. What does it mean? 2b vector that means I am increasing its magnitude, we have doubled its magnitude. Fine. So what does minus 2b mean? We have doubled the magnitude as well as directed it in an opposite manner. Done? Any doubts? Then note down. If a vector is multiplied, If a vector is multiplied, with a positive number, If a vector is multiplied with a positive number its magnitude changes. But its direction does not change. On the other hand, On the other hand if a vector is multiplied by, if a vector is multiplied by a negative number both its magnitude and direction changes. And draw these diagrams. a vector, minus a vector. Multiplied by minus one, direction has been changed, for the moment there is no change in magnitude. But if I multiply it by -2, then both direction and magnitude will change. Please draw all these diagrams.

Let’s take one better thing. Let’s us consider a vector and b vector. And angle between them is theta. There are two vectors and angle between them is theta. Okay? Now let’s see, if the angle between the vectors a and b is theta, then what should be the angle between a and –b vector? See here is the, a and b vectors, as I have kept here the blue marker. And if I multiplying it by minus b, what does it mean? That means I am rotating it by 180 degrees. So when the vector was over here, so what was the angle? Sir that was the angle theta, wasn’t it? And when I am changing it to minus b, then what would be its angle? 180 degree. So the vector came here and now shouldn’t we count this as an angle or not? If this angle is theta, so what about this angle my dear? 180 minus theta. Done? So that is a very important T&T, if the angle between a and b is theta, so then angle between a and –b is, π minus theta. 180 minus theta. So that means if this angle is 30 degrees, so how much would be this angle? 150 degrees. Please note down. If the angle between a and b is theta, so angle between a and –b will be, 180 minus theta. So now please understand how wonderfully we will use this concept. In our last class what we learnt is that if a vector is added to b vector it will give you the resultant vector and magnitude of resultant vector was what? Root of a square plus b square plus 2ab cos theta. What was the theta? Angle between the two vectors. Okay. So this was the resultant of addition. This was the resultant of addition. What if I am writing a vector minus b vector? So there would be a resultant of this as well. Now if the resultant of addition is r, so then the resultant of subtraction would be different. Right? So let us find, put the heading as subtraction of two vectors. So what we are planning, here we are planning to work out the value of a vector minus b vector.