Question

Let W be the subset of ℝ⁵ consisting of all vectors that are the same backwards as forwards. More precisely, a vector (v₁, v₂, v₃, v₄, v₅) i

Answer 1

After adding three vectors of equal magnitude but pointing in different directions, the two opposing vectors cancel each other out, leaving only the magnitude of the third vector which is 5 units.

Step-by-step explanation:

The question asks about adding three vectors of equal magnitude, but pointing in different directions. Vectors u, V, and W all have a magnitude of 5 units. Since vector u points to the northwest, and vector W points to the southwest, directly opposite of vector u, these two vectors will cancel each other out due to their opposing directions. Vector V, which is not opposed by any other vector, will therefore determine the magnitude of the resultant vector when all three are added together.

The resultant magnitude will thus be equal to the magnitude of vector V alone, since the contributions of vectors u and W cancel each other. Therefore, the magnitude of the resultant vector is 5 units.