Which of the following three vectors has the greatest magnitude: v + (−w), w − v, or
(−v) − (−w)?

All have same magnitude.

Step-by-step explanation:

Given that

Vector 1 = V+ (-W) = V - W

So the magnitude of vector 1, R₁

R₁ = V -W

For vector 2

Vector 2 = W - V  = W - V

So the magnitude of vector 2, R₂

R₂ = V -  W

For vector 3

Vector 3 = (-V) - (-W) = - V + W = W - V

So the magnitude of vector 3,

R₃ = W -V

So all have same magnitude.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

step-by-step explanation:

se a cavasery6