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Assignment #1 – Vector Algebra
1) Three field quantities are given by
P
= 2
a
x

a
z
Q
=
a
x

a
y
+ 2
a
z
R
= 2
a
x
 3
a
y
+
a
z
Determine
(a) An unit vector perpendicular to both
Q
and
R
(b) The component of
P
along
Q
(c)
(P+Q) x (PQ)
(d)
Q. R x P
2) Given the vector field (cylindrical coordinates)
H
=
ρ
z cos
φ
a
ρ
+ sin (
φ
/2)
a
φ
+
ρ
2
a
z
At point (1,
π
/3,0), find
(a)
H . a
x
(b)
H x a
θ
(c) The vector component of
H
normal to surface
ρ
=1
(d) The scalar compenent of
H
tangential to the plane z=0
3) Calculate
(a) the angle between the normals to the surfaces x
2
y+z = 3 and x logz –y
2
=4 at the point
of intersection (1,2,1)
(b) the angle at which the line x=y=2z intersects with the ellipsoid x
2
+ y
2
+ 2z
2
=10
4) Determine
(a) the divergence of these vector fields
P
= x
2
yz
a
x
+xz
a
z
Q
=
ρ
sin
φ
a
ρ
+
ρ
2
z
a
φ
+ z cos
φ
a
z
(b) the flux of
D
=
ρ
2
cos
2
φ
a
ρ
+
z
sin
φ
a
φ
over
the
closed
surface
of
the cylinder
0
≤
z
≤
1,
ρ
=4.Verify the divergence theorem for this case.
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This note was uploaded on 09/12/2010 for the course EE EE645 taught by Professor Ujin during the Spring '10 term at YTI Career Institute.
 Spring '10
 Ujin

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