Answer:
4, 1, 6, 2, 3, 5
Step-by-step explanation:
When you have so many to do, it is convenient to let a calculator or spreadsheet do the math for you. The attached calculated the sums. Then the magnitudes needed to be calculated from those.
The numbers listed in the answer section are the order in which the resultant vectors appear in the ascending order list. That is, (u+2v-w)/6 appears first in the list.
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Each resultant is found by adding the given vectors with the given coefficients. For example, consider the first one on the list:
... -1/2u +5v = (-1/2)(9, -2) + 5(-1, 7)
... = (-9/2 -5, +1 +35) = (-19/2, 36)
Then the magnitude of it is found by adding the components according to the Pythagorean theorem. For the resultant just computed, the magnitude is ...
... √((-19/2)² +36²) = √(90.25 +1296) = √1386.25 ≈ 37.23
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In the attached, matrix multiplication is used to compute all 6 resultants at once. The 6 resultant vectors are the answer to that multiplication. The magnitudes are computed from these results as above.
I get the magnitudes of the resultants (to 2 decimal places) to be ...
37.23, 3.89, 42.04, 28.50, 32.04, 41.10
