Calculus/Calculus 3

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Expert: - 9/5/2010


Question
Determine whether the points lie on a straight line,
a, A(2,4,2)  B(3,7,-2)  C(1,3,3)
b, D(0,-5,5) , E(1,-2,4), F(3,4,2)  

Answer
Take the points each asw (x,y,z).

Look at the difference in the x values.
For the set in a, the x values are 2, 3, and 1.l.
The difference in 3-2 = 1 and 1-3 = -2.
This means the second difference is -2 times the first difference.

Next, look at the y values, which are 4, 7, and 3.
7-4=3, so the second y difference should be -6.  This means the second y value should be 7-6=1, but it is 3.
This means that this is not on a line.

For the z values the fir st difference is -2-2 = -4.
Now -4*-2 = 8, so the second difference should be 8.
This means it should be -2+8 = 6, but it is 3, so again,
these points are not on a line.


For the second set of points, the x differences are 1 - 0 = 1 and
3 - 1 = 2, so the second difference should be twice the first.
Check out the differences on the y's at -5, -2, and 4 and
on the z's at 5, 4, and 2.  For both y and z, the second difference should be twice the first if the points are on a line.

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