Vector Functions

Question 1

What is the definition of the limit of a vector function?

Answer 1

If a limit exists then it is assumed the length and direction of r(t) approaches that of vector L

Question 2

When is a vector function continuous at a?

Answer 2

If lim r(t) = r(a)

Question 3

What is the formula for the set of Parametric Equations?

Answer 3

{r(t) + a(r’(t))}, where a is a real number.

Question 4

When can a vector function form a space curve?

Answer 4

When vector functions continuous and component functions need to be continuous and real valued

Question 5

What does r(t) represent in the context of a space curve?

Answer 5

position vector of point P(f(t), g(t), h(t))

Question 6

How is the vector equation of a line segment determined?

Answer 6

r(t) = (1-t)(x1,y1,z1) + t(x2,y2,z2)

Question 7

What is the unit tangent vector and how is it calculated?

Answer 7

Given direction of curve at point t
T(t) = r’(t) / |r’(t)|

Question 8

What is acceleration and velocity using vectors?

Answer 8

Acceleration is the derivative of velocity
therefore velocity is the integral of acceleration