; (recall that 
is the
third vector in the standard orthonormal basis
associated with the rectangular coordinates). Then the velocity of
the projectile is (c) 
.
.
.
, we denote by 
and 
the (planar) unit vectors given by
.
A circular motion can be described by an equation of
the form 
, where R is the radius
of the circle.
Then the speed of the motion at time t is \
(a) 
.
.
So the speed is
.
. Then its
rectangular coordinates is (b)
.
,
, and
of this point is
(a) 
.
,
and 
.
describes a sphere. The center of this sphere is (d) (2,-2,1).
The radius is (c) 3.
on both
sides:
.
Using the substitutions 
,
, 
and 
, we have 
.
Rewrite the above equation as 
, which gives
where 
and 
are given functions of t for t between
a and b. Then the arc length of C is given by
(c) 
.
.
Now
By an easy computation, we get
and hence
.