Final answer:
The direction of v₁ is approximately 307°, and the direction of v₂ is approximately -42° (counterclockwise from the positive x-axis).
Step-by-step explanation:
To determine the direction of vectors v₁ and v₂, we need to use the unit vectors i^ and j^ as reference points. The direction of v₁ can be determined by looking at the coefficients of i^ and j^. Since v₁ = -6.0 i^ + 8.5 j^, the direction of v₁ is 180° + tan⁻¹(8.5/-6.0) = 180° + 127° ≈ 307°. Similarly, the direction of v₂ can be determined by looking at the coefficients of i^ and j^. Since v₂ = -4.7 j^ + 4.3 i^, the direction of v₂ is tan⁻¹(4.3/-4.7) = -42° ≈ -42° (counterclockwise from the positive x-axis).