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True or false 1. If F =< P(x,y),Q(x,y) > and Py = Qx in an open region D, then F is conservative. 2. If F and G are vector fields, then curl(F ·G) = curl F ·curl G.

True or false 1. If F =< P(x,y),Q(x,y) > and Py = Qx in an open region D, then F is conservative. 2. If F and G are vector fields, then curl(F ·G) = curl F ·curl G.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...
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True or false

1. If F =< P(x,y),Q(x,y) > and Py = Qx in an open region D, then F is conservative.

2. If F and G are vector fields, then curl(F ·G) = curl F ·curl G.

3. It is impossible to find three non-zero three-dimensional real vectors u, v, and w such that
(v ·w)(v ·u) = 0 while simultaneously (v ×w) ·(v ×u) = 0.

4. Recall that κ(t) denotes the curvature of a curve. If κ(t) = d for all t, with d ≥ 0 , then the
curve is a straight line.

 

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