Consider a spacecraft orbiting a space station that is at the point (5,7). The position function of the spacecraft is 3 t+1 r(t) = (2+1, 3+1, 4 + The spacecraft is short on fuel. Since they are in space there is no friction. Therefore, if they cut their engine they will continue to travel in the direction of their velocity. When should they stop their engine so that they reach the space station? What is there position when they stop their engine and what will their new position function be?

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