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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.

Respuesta :

We will solve as follows:

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

[tex]A=4i-j+7k[/tex][tex]B=16i-10j+10k[/tex]

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:

[tex]v=\frac{B-A}{t_1}\Rightarrow v=\frac{(16-4)i+(-10+1)j+(10-7)k}{3}[/tex][tex]\Rightarrow v=\frac{12i-9j+3k}{3}\Rightarrow v=4i-3j+k[/tex]

Third: We now determine the value of C:

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

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

[tex]C=(20,-13,11)[/tex]

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