Question

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

(−v) − (−w)?

Answer 1

All have same magnitude.

Explanation:

Given that

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

So the magnitude of vector 1, R₁

`R_1=√((V-W)^2)`

R₁ = V -W

For vector 2

Vector 2 = W - V = W - V

So the magnitude of vector 2, R₂

`R_2=√((W-V)^2)`

R₂ = V - W

For vector 3

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

So the magnitude of vector 3,

`R_3=√((W-V)^2)`

R₃ = W -V

So all have same magnitude.