Understanding Engineering Mathematics

O

A P

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n

a

Figure 11.18Vector equation of a plane.

is the general equation for a plane. Ifn=αi+βj+γkthen in terms of coordinates this is
αx+βy+γz=ρ

Exercise on 11.12

Sketch the path described by the position vector

f(t)=costi+sintj+k

astvaries.

Answer

x

z

1

(^0) y

11.13 Differentiation of vector functions

The idea of a vector functionf(t)of traises the question of its rate of change ast
varies. In the case of the projectile of Section 11.12, this rate of change would represent
the velocity of the projectile at the timet. If you look back at the definition of the
derivative on page 231, the following definition will probably now make sense to you.
We are essentially applying the definition to each component of the vector function. The
derivative of a vector function f.t/,with respect totis defined by

df(t)

dt

=lim

h→ 0

(

f(t+h)−f(t)

h

)

Problem 11.10

Show that the derivative of a constant vector is zero.