00:01
Okay, so in this problem you're given four vectors, all of their magnitudes, and all the angles with the coordinate system, and you're asked to find the result in vector if you add them all up using the component method, which basically means you to break it down into all the x and y pieces and add those all together.
00:14
So it kind of helps think these like right triangles and use trigonometry.
00:18
So if we start with a, vector a makes a 60 degree angle with the x -axis.
00:24
So to find the vertical component, which is the y component, so y of a, you just need to take the sign, of the angle, which is 60 degrees, and multiply that by the magnitude, which is given is 2 .25 in the problem.
00:37
And if you plug that in your calculator, make sure you're in sine mode.
00:41
If you're using a calculator that it has a radian mode, you'll get 1 .948 as the vertical component, and then the x component of a will just be the same thing, but use the cosine function instead.
00:55
So, cosine of 60 degrees times 2 .25.
00:58
And you'll find that that is equal to 1 .125.
01:07
So very similarly, we can find the components for vector b.
01:11
In this case, the vertical component will be negative because you can see that vector b extends below y equals zero on the coordinate plane, so this would be negative sign of 20 degrees times the magnitude of vector b, which is 6 .35.
01:26
And again, if you type that into your calculator, we will find that the answer is negative 2 .172.
01:38
And then same thing for, sorry, this is y of b, and then same thing for x of b.
01:44
In this case, it's still positive.
01:45
So you use cosine of 20 degrees times 6 .35.
01:51
And then cosine of 20 degrees times 6 .35.
01:54
The value is 5 .967.
02:02
Okay, so now we'll do vector c.
02:04
And this one's a little bit different because you can see that the, angle 36 degrees is drawn to the y -axis, not to the x -axis.
02:10
So remember, so -kotoa, the sign function gives you the ratio of the opposite side over the hypotenuse, whereas the cosine gives you the ratio of the adjacent side over the hypotenuse.
02:21
So we'll actually start by finding the horizontal component this time.
02:24
So x of b is going to be equal to sine, or x of c, sorry, sine of 36 degrees, times the magnitude of vector c, which is 5 .47 centimeters.
02:37
So sign of 36 times 5 .47 is going to be equal to 3 .215...