 Let's solve a couple of questions on vectors, magnitude and direction. Here we have a bear which is applying a force on a tree by rubbing its back on it. And here we have the bear, there's also a cub. Now the strength of the force is 25 Newtons and the direction is 35 degrees to the east from the northward direction relative to the tree. And here are a few vectors, you can see there are four vectors where the magnitude of A and C is equal and it's equal to 25 Newtons and the magnitude of B and D is equal and it's equal to 35 Newtons. We need to think about which vectors can represent the force that the bear applies to the tree. And we can choose all the answers that apply, there can be more than one correct answer. Again, as always pause the video and give this one a try first. Alright, hopefully you have given this a shot. Now let's think about how do we define a vector? We define a vector by its magnitude and its direction, by magnitude and direction. And we know the magnitudes of all of these four vectors, we also know the direction of each of these four vectors. And any vector out of these four which has the right correct magnitude and correct direction to the force that the bear is applying to the tree will be the right answer. Now we know that the magnitude of the force that the bear is applying, magnitude of that force vector, it's 25 Newtons and it is, the direction is 35 degrees to the east from the northward direction. So this really means, this really means, we have a north direction like this and the vector, the force vector, it's inclined at an angle of, it's making an angle of 35 degrees, it's making an angle of 35 degrees to the east. This angle right here, this angle right here is 35 degrees. So this is 35 degrees to the east from the northward direction. So the vector should be making an angle of 35 degrees. And the magnitude of the vector, the magnitude should be 25 Newtons. So out of these four vectors, we see the magnitude of the vectors A and C, that is 25 and A and C both are making an angle of 35 degrees to the east from the northward direction. It doesn't really matter where the vector is starting from and where it is ending. As long as the magnitude and direction of the vector is the same to the force that the bear is applying to the tree, those two vectors will be the right one. So here, this is A and C. B and D are wrong because their magnitude is different, it's 35 Newtons and also the angle that they are making, they are making an angle of 25 degrees to the east from the northward, which is not the direction of the force that the bear is applying to the tree. Alright, now let's move on to the next question. Here we have two boats, A and B, which are participating in a race. Their velocities are represented by vectors A and B, which option best describes the meaning of the following statement. So this is a statement, it says vector A is equal to vector B. We need to choose one answer out of these three options. Now we can try this by again going back to what a vector is. A vector, a vector has both a magnitude, both a magnitude and a direction. So if we say that vector A is equal to vector B, then what we are really saying is that the magnitude of vector A, magnitude of vector A and the direction of vector A, it is equal, this is equal to the magnitude of vector B and the direction of vector B. When we write vector A equal to vector B, both of these things, magnitude and direction, both of them have to be equal for us to say that these two vectors are equal. So in this case, the vector is velocity, we have a velocity vector and the velocity vector has its magnitude, which is really just the speed that is the magnitude and it has its own direction, it has its own direction. So when these two vectors, when these two velocity vectors are the same, it means both the boats are moving with the same speed and in the same direction. Now the first option says the two boats move at the same speed in the same direction. Yes, that is what it means for two vectors to be equal, so option A is right. Option B says the two boats move at the same speed but not necessarily in the same direction. This is wrong because for two vectors to be equal, both the magnitude and the direction has to be the same and option C is also really wrong because it says that the boats are moving in the same direction but not necessarily at the same speed. Again, the speed has to be the same and so does the direction. So here option A is correct. You can try more questions from this exercise in the lesson and if you are watching on YouTube, do check out the exercise link which is added in the description.