Flow Lines The flow lines (or streamlines) of a vector field are the paths followed by a particle whose velocity field is the given vector field. Thus the vectors in a vector field are tangent to the flow lines. (a) Sketch the vector field 𝐅(x, y)=𝐢 x 𝐣 and then sketch some flow lines. What shape do these flow lines appear to have? (b) If parametric equations of the flow lines are x=x(t), y=y(t), what differential equations do these functions satisfy? Deduce that d y / d x=x. (c) If a particl
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Flow Lines The flow lines (or streamlines) of a vector field are the paths followed by a particle whose velocity field is the given vector field. Thus the vectors in a vector field are
Flow Lines The flow lines (or streamlines) of a vector field are the paths followed by a particle whose velocity field is the given vector field. Thus the vectors in a vector field are tangent to the flow lines. (a) Sketch the vector field 𝐅(x, y)=𝐢 x 𝐣 and then sketch some flow lines. What shape do these flow lines appear to have? (b ...
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