Problem 2.34
Vector field E is given by
E
5R cos
R
12
sin cos 3 sin
R
Determine the component of E tangential to the spherical surface R
P 2 30 60 .
2 at point
Solution: At P, E is given by
E
12
sin 30 cos 60 3 sin 60
2
8 67 1 5 2 6
R
5
2 cos 3
Problem 2.33
A given line is described by the equation:
x 1
y
Vector A starts at point P1 0 2 and ends at point P2 on the line such that A is
orthogonal to the line. Find an expression for A.
Solution: We first plot the given line.
y
P1 (0, 2)
B
A
P2 (x,
Problem 2.32 Finde a vector G whose magnitude is 4 and whose direction is
perpendicular to both vectors E and F, where E x y 2 z 2 and F y 3 z 6.
Solution: The cross product of two vectors produces a third vector which is
perpendicular to both of the ori
Problem 2.17 When sketching or demonstrating the spatial variation of a vector
ﬁeld, we often use arrows, as in Fig. 2—25 (P117), wherein the length of the arrow
is made to be proportional to the strength of the ﬁeld and the direction of the arrow
is the
Problem 2.9 Find an expression for the unit vector directed toward the origin from
an arbitrary point on the line described by x 1 and z 2.
Solution:
An
arbitrary
point
on
the
given
line
is
1 y 2 . The vector from this point
to 0 0 0 is:
2z
x yy
A x 0