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A space shuttle is moving in a straight line and is traveling at a constant speed. It takes 3 hours to get from A to B and 1 hour to get from B to C. Relative to a suitable set of axes, A is the point (4,-1,7) and B is the point (16,-10,10). Find the coordinates of C.

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We will solve as follows:

First: We will use the i, j, k vector notation to describe each point as a vector:


A=4i-j+7k
B=16i-10j+10k

Now, we have that the time it takes to get from A to B is 3 hours (t1). And the time it takes from B to C is 1 hour (t2).

Second: We determine the speed from A to B:


v=(B-A)/(t_1)\Rightarrow v=((16-4)i+(-10+1)j+(10-7)k)/(3)
\Rightarrow v=(12i-9j+3k)/(3)\Rightarrow v=4i-3j+k

Third: We now determine the value of C:


C=B+vt_2\Rightarrow C=(16+4)i+(-10-3)j+(10+1)k
\Rightarrow C=20i-13j+11k

So, we would have that the coordinates of C are:


C=(20,-13,11)

User Mjimcua
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