Final answer:
To find vectors v₁ and v₂ that satisfy the given conditions, calculate their magnitudes based on the given information and find the vector that is perpendicular to v₁.
Step-by-step explanation:
To find two vectors v₁ and v₂ whose sum is <-5, 5>, we first need to find the magnitudes of both vectors. Since v₁ is parallel to <-5, -4>, its magnitude will be the same as that of <-5, -4>, which is √((-5)^2 + (-4)^2) = √41. To find v₂, we want it to be perpendicular to v₁, which means their dot product should be 0. So, we have the equation v₁ · v₂ = (-5)(-5) + (-4)(-4) = 41 = 0. Solving for v₂, we get v₂ = <-4, 5>. Therefore, v₁ = √41 * <-5, -4> and v₂ = <-4, 5> will satisfy the given conditions.