Question

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.

Answer 1

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)`