Final answer:
To find the direction of the sum of vectors v and u, add their components and use the inverse tangent function. The direction of the sum is D) 81.87°.
Step-by-step explanation:
To find the direction of the sum of vectors v and u, we can add their components and then use the inverse tangent function to find the angle.
The components of v are 2 for the x-axis and 3 for the y-axis, while the components of u are -1 for the x-axis and 4 for the y-axis. Adding the x-components gives 2 + (-1) = 1, and adding the y-components gives 3 + 4 = 7.
So, the sum of v and u is a vector with components 1, 7. Using the inverse tangent function with the ratio of the y-component to the x-component, tan⁻¹(7/1) ≈ 81.87°.
Therefore, the direction of the sum of v and u rounded to the nearest hundredth of a degree is D)81.87°.