Q6 (a) Sketch the vector and scalar fields. Describe the nature of vector fields. Find also Curl and divergence in parts (i)-(iii). In parts (iv) and (v), find a unit normal to the given surface at a point of your choice. (i) F=x i-yj (ii) G=x i-yj (iii) H=cos(x +y)i+sin(x –y)j, (iv) f =4x – 3y +pz for –p

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Chapter2: Second-order Linear Odes
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Q6 (а)
Sketch the vector and scalar fields. Describe the nature of vector fields.
Find also Curl and divergence in parts (i)-(iii). In parts (iv) and (v), find a
unit normal to the given surface at a point of your choice.
(i) F=x i-yj (ii) G=x i-y j
(iii) H=cos(x +y)i+sin(x –y)j,
||
(iv) f =4x – 3y +pz_for -p <x ,y <p .
%3D
(v) g = px² +5y² for -p <2x,2y <p.
http://user.mendelu.cz/marik/EquationExplorer/vectorfield.html
https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/
(b)
Find the parametric form of (i) the circle x?+y? =p² (ii) the ellipse
2
2
1 (ii) the straight line joining the points 1,2,4 and 2, p,7 .
p?
25
Transcribed Image Text:Q6 (а) Sketch the vector and scalar fields. Describe the nature of vector fields. Find also Curl and divergence in parts (i)-(iii). In parts (iv) and (v), find a unit normal to the given surface at a point of your choice. (i) F=x i-yj (ii) G=x i-y j (iii) H=cos(x +y)i+sin(x –y)j, || (iv) f =4x – 3y +pz_for -p <x ,y <p . %3D (v) g = px² +5y² for -p <2x,2y <p. http://user.mendelu.cz/marik/EquationExplorer/vectorfield.html https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/ (b) Find the parametric form of (i) the circle x?+y? =p² (ii) the ellipse 2 2 1 (ii) the straight line joining the points 1,2,4 and 2, p,7 . p? 25
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