Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
Equation of a Space Curve
Let P (x,y,z) be any point in space then its position vector is
OP
r
x i
y j
z k
If x = x(t), y = y(t) and z = z(t) are functions of a scalar variable
t then
r r (t)
describes
a
curve
in
space
called
the
space
curve.
Note 1:
d r
dt
represents
the
velocity
v
(rate
of
change
of
position
with
which
the
ter min al po int
of
r
describes the
curve )
Note 2:
d r
dt
is
along
the
direction
of
the
tan gent
to
the
space
curve
at
P (x, y, z)
Note 3:
The
unit
tan gent
vector
to
the
space
curve
is
denoted by
t
and
is given by
d r
t
dt
d r
| |
dt
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