1.5 pts Question 7 The FTOLI (Fundamental Theorem of Line Integrals) says: (you may select one or more correct answers) The work done by a gradient vector field is independent of path. The line integral of a gradient vector field depends only on the initial and terminal points of the path. The work done by any vector field is independent of path. The work done by a gradient vector field is always zero. None of these.
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Step 1: The Fundamental Theorem of Line Integrals states that if F is a gradient vector field, then the line integral of F along a path depends only on the initial and terminal points of the path. Show more…
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Hoan N.
The FToLI (Fundamental Theorem of Line Integrals) says: (You may select one or more correct answers) The work done by a gradient vector field is always zero. The work done by any vector field is independent of path. None of these. The line integral of a gradient vector field depends only on the initial and terminal points of the path. The work done by a gradient vector field is independent of path.
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Choose all correct statements. The line integral of a vector field along a closed path is zero. The line integral of a scalar function along a path C does not change if the direction of the path is reversed. Divergence measures the tendency of a vector field to swirl around a point. The work done on a particle when it moves along a path C in a conservative vector field is zero. Gravitational and electric fields are conservative vector fields. In a vector field, the sum of the kinetic energy and the potential energy of a particle is always a constant. If the line integral of a vector field along a curve C is zero, then the curve is always perpendicular to the vector field. Curl and divergence of a vector field are vectors.
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