Chapter 12.6, Problem 50PPSE

Solution

To find: To check if the second helicopter ends in the same place as the first helicopter.

The second helicopter would end in the same place as the first helicopter.

Given information:

Given, a helicopter starts at $\left(0,0\right)$ and makes three legs of a flight represented by the vectors $〈10,10〉,〈5,-4〉,〈-3,5〉$ in that order. Another helicopter starts at $\left(0,0\right)$ and flies the same three legs in a different order.

Calculation:

The final position of the first helicopter is given by:

  $〈10,10〉+〈5,-4〉+〈-3,5〉=〈10+5-3,10-4+5〉=〈12,11〉$

According to properties of vectors, addition of vectors is both associative and commutative.

Hence, the order of addition is not important in vector addition.

So whatever order the second helicopter takes the legs, it would end in the same place as the first helicopter.

Conclusion:

The second helicopter would end in the same place as the first helicopter.