Addition of two vectors. Case one. Case one. If we have magnitudes of two vectors. Magnitude of two vectors and angle between them. So we are planning to work out the addition or we are planning to work out about the resultant force, resultant vector in fact, if you know the magnitude of two vectors and the angle between them. Say I know one vector a having magnitude a and the another vector is b having magnitude b and the angle between them theta. If I want to find the resultant of a and b, that mean I want to find a vector plus b vector and their resultant. Done? We have seen the triangle law of vector addition. What we do is, we either shift one or both the vectors parallel, so let’s shift b parallel to itself and rearrange it like that. This is a vector and this is b vector. Now class, see carefully. If I draw an extended line here, this angle will also be the theta. See carefully because I am shifting b parallel, so the new b vector is also is parallel to the previous one, so that this angle is theta, this angle will also be the theta. Any doubts? Okay. Now we know that this is the resultant vector. This is the resultant vector. Say the resultant is having the magnitude r. so what we are planning is actually, we are planning to find the magnitude of resultant vector. We want to find a + b; r vector. So how we get the complete information about the r vector? With the magnitude of r vector and with the direction of r vector. Done? So first we will try to work out the magnitude of r vector. Okay. See we will use the properties of triangle. Now class see it very carefully. An extended line, this point here, from here draw a perpendicular. Perpendicular is 90 degrees. Okay? You can notice here carefully. Now see lets concentrate on two different angles. Triangles. X, Y, Z and T. See carefully triangle XTY is right angled triangle. Similarly triangle ZTY is also the right angled triangle. And in these two triangles we can directly use the ordinary ideas that we know about a right angled triangle. Done? Okay. Let’s take triangle ZTY. Can I write ZT as b cos theta. This is b vector having magnitude b. this can be considered as the horizontal component of b vector, and the horizontal component of b vector will become b cos theta. See it carefully. Done? Only concentrate on b vector and think about the horizontal component of b vector. If this is b vector this is angle theta, so its horizontal component will be b cos theta. Done. Similarly YT will be the vertical component and it will be sine theta. Okay. Class now see carefully.