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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2012 • Question 5

Question

Math 6510 • Differentiable Manifolds Fall 2012 • Question 5

Find the following bracket of two vector fields in \(\mathbb {R}^3\) \[ \left [ (x+y)\frac {\partial }{\partial x}+z\frac {\partial }{\partial y}, yz\frac {\partial }{\partial y}+x^2\frac {\partial }{\partial z} \right ]. \]

Raw LaTeX

Find the following bracket of two vector fields in \(\R^3\)
\[
  \left[
    (x+y)\frac{\partial}{\partial x}+z\frac{\partial}{\partial y},
    yz\frac{\partial}{\partial y}+x^2\frac{\partial}{\partial z}
  \right].
\]

Topic Tags

Left-Invariant Vector Fields Vector Fields and Flows