Question

Suppose F⃗ (x,y)=⟨ex,ey⟩ and C is the portion of the ellipse centered at the origin from the point (0,1) to the point (3,0) centered at the origin oriented clockwise. (a) Find a vector

Answer 1

To find the vector F⃗ (x,y)=⟨ex,ey⟩, substitute the values of x and y into the equation. The work done by force vector F₁ can be calculated using the equation W = F⃗ ⋅ d⃗, where F⃗ is the force vector and d⃗ is the displacement vector.

Step-by-step explanation:

To find a vector F⃗ (x,y) given by ⟨ex,ey⟩, we need to substitute the values of x and y into the equation. In this case, x = e and y = e. Hence, the vector F⃗ (x,y) is given by the equation F⃗ (x,y)=⟨e^2,e^2⟩.

To find the work done by F₁, we need to use the equation for work, which is defined as the dot product of force and displacement. In this case, the force F₁ is given by F₁ = (3 N)Î + (4 N)Ĵĵ and the displacement is from (0 m, 0 m) to (5 m, 6 m). The work done is given by the equation W = F⃗ ⋅ d⃗, where F⃗ is the force vector and d⃗ is the displacement vector. By substituting the given values, we can calculate the work done.