0:00
Hi there.
00:01
So for this problem, we need to add these two vectors together and find the direction of the sum of the vectors.
00:10
So for this, we are given the vector 1, which has a magnitude of 30, and its direction is given with respect to the x direction, and that is 225 degrees with respect to the horizontal, and the vector 2, which has the magnitude of 40, and the direction is also given, and that is 315 degrees.
00:36
Now, to add these two vectors together to form a vector that we're going to call to simply be, we need to, well, we need to pass these two vectors into a component form.
00:56
So to do that, we write, for example, the vector one is going to be, its magnitude and since the angle we assume it that is given with respect to the horizontal then the x component is given by the cosine of the angle in the in this case for the first one is 225 in the x component and the sign of that same angle in the white component now we have something similar for the vector b2 so that is 40 times the cosine of 315 degrees in the x component and the sign of 350 degrees in the y component.
01:44
So now that we need to add together these two vectors, we will obtain the following.
01:51
So for the x component, we obtain 30 times the cosine of 225 degrees, and these plus 40 times the cosine of 315 degrees.
02:07
And this in the x direction.
02:10
And this plus what we will have for the y component, so that will be the y component of the vector 1 that we know is given by the sign of this, plus 40 times the sign of 350 degrees.
02:28
Now, using our calculator, we obtained the following resultant vector, and that is that the x component is 7 .071 in the x direction and minus 49 .5 in the y direction.
02:51
Now, we know that this vector is in the fourth quadrant, and that's because we know that is, in the fourth quadrant, the x component should be positive, like in our case, but the white component is negative like we have in here.
03:14
So the vector should be something like this.
03:19
Now, we can obtain this angle right here, and then add to that angle to 170 degrees so that we will obtain.
03:41
Its direction with respect to the horizontal.
03:46
So with that said, we can use the tangent of theta.
03:51
We can use the trigonometry for this triangle right here.
03:56
So as you can see in here, for this case, it should be the x component of this vector divided by the y component of this vector.
04:08
This will give us this angle in here that we're going to call the angle teta...
