11.1: Vector Fields
- Page ID
- 144358
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- Sketch the vector field \(\mathbf{F}(x, y) = (x, y)\), then roughly sketch the flow line through the point \((1, 1)\).
- Sketch the vector field \(\mathbf{F}(x, y) = \mathbf{j}\), then roughly sketch the flow line through the point \((1, 1)\).
- Sketch the vector field \(\mathbf{F}(x, y) = -x\mathbf{i} - y\mathbf{j}\), then roughly sketch the flow line through the point \((1, 1)\).
- Sketch the vector field \(\mathbf{F}(x, y) = (-y, x)\), then roughly sketch the flow line through the point \((1, 1)\).
- Sketch the vector field \(\mathbf{F}(x, y) = x\mathbf{i} - y\mathbf{j}\), then roughly sketch the flow line through the point \((1, 1)\).
- Sketch the vector filed \(\mathbf{F}(x, y) = (y, \cos x)\), then roughly sketch the flow line through the point \((1, 1)\).
- Sketch the vector field \(\mathbf{F}(x, y) = (x(1+y), -(x+y))\), then roughly sketch the flow line through the point \((1, 1)\).
- Sketch the vector field \(\mathbf{F}(x, y, z) = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}\), then roughly sketch the flow line through the point \((1, 1, 1)\).