Suppose that $\int _ { C _ { 1 } } \vec { F } \cdot \overline { d r } = 4 , \int _ { C _ { 2 } } \vec { F } \cdot \overline { d r } = 3 , \int _ { C _ { 3 } } \vec { F } \cdot \overline { d r } = 16$ and $\int _ { C _ { 4 } } \vec { F } \cdot \overline { d r } = - 1$ where C₁ is the line joining (0, 0)to (1, 0), C₂ is the line joining (0, 0)to (3, 0), C₃ is the line joining (0, 0)to (0, 1)and C₄ is the line joining (0, 1)to (0, 2).
Determine, if possible, the value of the line integral of $\vec{F}$ along the line from (0, 1)to (1, 0).If the value cannot be determined, say so.

Question

Suppose that

\int _ { C _ { 1 } } \vec { F } \cdot \overline { d r } = 4 , \int _ { C _ { 2 } } \vec { F } \cdot \overline { d r } = 3 , \int _ { C _ { 3 } } \vec { F } \cdot \overline { d r } = 16

and

\int _ { C _ { 4 } } \vec { F } \cdot \overline { d r } = - 1

where C₁ is the line joining (0, 0)to (1, 0), C₂ is the line joining (0, 0)to (3, 0), C₃ is the line joining (0, 0)to (0, 1)and C₄ is the line joining (0, 1)to (0, 2).
Determine, if possible, the value of the line integral of

\vec{F}

along the line from (0, 1)to (1, 0).If the value cannot be determined, say so.

Quizplus · Accepted Answer

The Answer of Suppose that $\int _ { C _ { 1 } } \vec { F } \cdot \overline { d r } = 4 , \int _ { C _ { 2 } } \vec { F } \cdot \overline { d r } = 3 , \int _ { C _ { 3 } } \vec { F } \cdot \overline { d r } = 16$ and $\int _ { C _ { 4 } } \vec { F } \cdot \overline { d r } = - 1$ where C₁ is the line joining (0, 0)to (1, 0), C₂ is the line joining (0, 0)to (3, 0), C₃ is the line joining (0, 0)to (0, 1)and C₄ is the line joining (0, 1)to (0, 2). Determine, if possible, the value of the line integral of $\vec{F}$ along the line from (0, 1)to (1, 0).If the value cannot be determined, say so.

Suppose That And ∫C4F⃗⋅dr‾=−1\int _ { C _ { 4 } } \vec { F } \cdot \overline { d r } = - 1∫C4​​F⋅dr=−1

Suppose That And $\int _ { C _ { 4 } } \vec { F } \cdot \overline { d r } = - 1$