 Let's solve a question on scalar multiplication of vectors. Here we have a vector B which has a magnitude of 10 units and it makes an angle of 30 degrees with a positive x-axis. We need to figure out the magnitude and direction of minus 3 into P. Give that direction as an angle measure between 0 and 360 degrees. Alright, as always pause the video and try and attempt this question on your own. Okay, hopefully you have given this a shot. Now let's try and think about what happens to a vector when you multiply it with a scalar. And over here, we are multiplying it with a negative scalar with a negative scalar. So let's say our negative scalar is generally we can say it's minus a when we multiply any vector with minus a, it could be minus 1, minus 2, minus 3, here we have minus 3. What happens to the magnitude? What happens to the magnitude is magnitude, the new magnitude, the new magnitude of a vector. This is a times, a times the old, old magnitude. So the length of the new vector will be a times the length of the old vector. And what happens to the direction? Well we are multiplying it with a negative scalar. So direction reverses by 180 degrees. Okay, now we are multiplying it with minus 3. So the new magnitude of the vector of the new magnitude, it will be 3 times the old magnitude and minus 3B's direction will be reversed by 180 degrees. So let's try and see what that could look like. Here we have the coordinate axis and here we have the original B vector with a magnitude of 10 and it's making an angle of 30 degrees with the positive x-axis. We can see it's making an angle of 30 degrees. And we can say that this is the magnitude is 10. So now the new vector, the new vector's magnitude will be 3 times 10, it will be 30, 30 units. So the length, the length should be 3 times this vector. And the direction we will reverse it by 180 degrees. So the new vector could look somewhat like this. The length, the magnitude is 3 times the old one and we have reversed it by 180 degrees. So now the angle that the new vector is making, this will be slightly over here, the angle that the new vector is making, it will be this 180 plus this 30, it will be a combination of both, 180 plus this 30 and the new angle would be 210 degrees. So we can write that over here. We can write this, the magnitude, the magnitude is 30, 30 units and the new angle that it is making, the direction is 210 degrees from positive x-axis, from positive x-axis.