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Hello everybody, in this video i'm going to be showing you how to solve the exercise 40 in chapter 13, section 4 of calculus early transcendentals.
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Now in this problem, they give us three points, a, with coordinates 3, 2, and 1, b with coordinates 5, 4, and 7, as well as c with coordinates 9, 8, and 19.
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And they want us to verify whether or not a, b, and c are collinear points.
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Now to solve this, let's first make an equivalence.
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We have the a, b, and c are co -linear.
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If and only if, the vectors, ab, and ac, have a cross product that's equal to the zero vector.
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And this is essentially just a restatement of theorem 13 .3, but it is explicitly worked out in exercise 39.
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So if you're uncomfortable with the statement, i would encourage you to look at that problem and sort it out for yourself.
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So to prove that a, b, and c are collinear, what we want to do is, or to verify whether or not they're collinear.
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We want to verify whether or not a, a, c is equal to zero.
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Let's start by finding the vectors ab and ac.
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Ab is going to have the components of b subtracted from the components of a.
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So we have that this is equal to 5 minus 3, with 4 minus 2, and then 7 minus 1.
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And this is equal to 2, 2, 6...