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A7001

Let r= ‏ند‎ + yj +zk and r=|| r ||,let ‏كر‎ be a differentiable function of one variable,
then show that Vf(r) = LO;

r
Find V.(V x F) and Vx(V x F) where F(x, y,z) = €` 7 + 4xe” j - € 4.

Module VI
Answer any three questions, each carries5 marks.

xy
+y

Use Green’s Theorem to evaluate [108(1- y)dx - 0
ಸ

triangle with vertices (0,0), (2,0) and (0,4).
Evaluate the surface integral 1 xzds ,where ois the part of the plane x+ y+z=1

ச

~ C is the

that lies in the first octant.
Using Stoke’s Theoremevaluate [Far where F(x, y,z) = ‏زمر‎ + 4x? y?j ೫೫, C
1

is the rectangle 0 < x > 1,0 < 9 <3in the plane 2 = ‏ہر‎

Using Divergence Theorem evaluate | | F.nds where

F(x, 1, 2) = थ + 107 + 2, ೮15 the surface of the cylindrical solid bounded by
2 + 12 =4,2=0 and 2 4.

Determine whether the vector fields are free of sources and sinks. If it is not,
locate them

(1) (1 + 2)7 - 2 + 1114 (ii)xyi-2xy j+y?k

11.

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