Answered: True or false 1. If F =< P(x,y),Q(x,y)…

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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