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.

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step-by-step explanation:

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