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Today we're going to determine whether the points a equals 321, b equals 547 and c equals 9 819 are co -linear.
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Geometrically three points are co -linear if they lie on the same line.
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This is some line in r3 and if we can put a line that goes through all of them then they are a co -linear.
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What this also means is that a vector, say you here, and v here are scalar multiples of each other so one might be able to write u equals lambda v for some non -zero constant and lambda will be real in order to do this we will construct two vectors first we will construct bc bc which is c minus b which is nine eight 19 minus 5, 4, 7.
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I choose this example to make the numbers we're dealing with smaller.
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So 9 minus 5 is 4.
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8 minus 4 is 4 and 19 minus 7 is 12.
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So this is our first factor that we're just going to call you.
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Now our next vector that we're going to create, let's choose ab, which is b minus a, which is 5, 4, 7, subtract 3, 2, 1.
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5 minus 3 is 2, 4 minus 2 is 2, and 7 minus 2 is 6, and this is v.
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Now, trivially, we can see that 2v equals u.
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But in all examples, it may not be so easy to see...