SOLVED:Sketch a few flow lines'of the given vector field. 𝐅(x, y, z)=(y,-x, 0)

SOLVED: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) Use a sketch of the vector field 𝐅(x, y)=x 𝐢-y 𝐣 to draw some flow lines. From your sketches, can you (b) If parametric equations of a flow line are x=x(t) , y=y(t), explain why these functions satisfy the differ- ential equations d x / d t=x and d y / d t=-y . Then solve the differen

SOLVED: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) Use a sketch of the vector field F(x, y)=x 𝐢-y 𝐣 to draw some flow lines. From your sketches, can you guess the equations of the flow lines? (b) If parametric equations of a flow line are x=x(t) y=y(t), explain why these functions satisfy the differential equations d x / d t=x and d y