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In this video, i'm going to be doing an example on working with vectors.
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Okay, so what i have is three vectors.
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I have vectors a, b, and c.
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And i know that vector a has a magnitude of a.
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And it's at an angle theta a equals 48 degrees with respect to the positive x axis.
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I have vector b.
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Vector b has a magnitude of b.
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And it's at an angle of theta b equals 70 degrees with respect to the x -axis, the positive x -axis.
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And i have vector c.
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The magnitude of vector c is 5 .11, and that's at an angle of theta -c equals 269 .2 degrees with respect to the positive x -axis.
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So let's just draw those vectors, quickly.
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I have vector a, which is at 48 degrees.
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So that's theta a.
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A.
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I have vector b, which is at 70 degrees.
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B, and that's that 70 degrees, theta b.
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And i have vector c, which is at negative, or 269, sorry, 0 .2 degrees.
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And that's there.
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Right, and we're given some other relationships.
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I am told that the magnitude of vector a equals the magnitude of vector b.
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And i'm told that vector c equals vector a minus two times vector b.
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Right, and what we want to find is the magnitudes of vectors a and b, keeping in mind that the magnitude is going to be equal.
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And the first thing we want to do with working with vectors is to break them down into their components.
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In this case, we're working with two -dimensional vectors, so each is going to have an x and a y component.
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All right.
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So vector a can be written as a magnitude of the vector times the cosine of the angle in the x direction, so that was cosine of 48x, plus the sign of that angle, so sign of 48y.
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And numerically, that is a time...