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Hello, hello.
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In this question we're given this vector diagram, and we're told that these two vectors have the same magnitude of 12 .6 meters, but the theta 1 and theta 2 are different.
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And we're asked to find the x and y components as well as the magnitude and direction of the resultant vector r.
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So in order to do this, we're going to go ahead and break both of these down into their x and y components.
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So i'm going to have some ax and ay, and then i'm going to also have some bx and by.
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And i know that rx, my resultant in the x direction, is going to just be ax plus bx, and these are as vectors.
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And then my resultant in the y direction, ry, is going to be ay plus by, also as vectors.
00:45
As scalars, we have to take into account direction.
00:48
So rx, well, ax goes in the positive x direction, it's going out to the right, but bx goes to the left.
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So i'm going to have to subtract bx there.
00:57
And then in the y direction, they both point up, so it's just going to be ay plus by.
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So what is ax? well, ax is going to be the vector value of a, so the whole thing, times the cosine of theta 1, so just this component down here.
01:15
And then i have to subtract bx, but it's kind of weird, what does that mean in terms of theta 2? so let's go ahead and do some geometry.
01:22
This is going to be our angle theta 1 here.
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And so this angle here, which i'll call rho, rho plus theta 2 plus theta 1 is going to be 180 degrees.
01:36
So rho is going to be 180 minus the sum of these two, so 180 minus 136, which is 44 degrees...