A vector function is simply a function whose domain is a set of real numbers and whose range is a set of vectors

Vector function (definition)

The component functions of this vector equation are,

f(t) = t³

g(t) = ln(3-t)

h(t) = √t

and the domain of r is the interval,

[0,3)

since ln(0) is undefined and the square root of a negative number is also undefined

f(t) = t³

g(t) = ln(3-t)

h(t) = √t

and the domain of r is the interval,

[0,3)

since ln(0) is undefined and the square root of a negative number is also undefined

What are the component functions of the vector function,

r(t) =

what is the domain of r?

r(t) =

what is the domain of r?

The limit of a vector function is defined by taking the limits of its component functions

How is the limit of a vector function defined?

The limit of r is the vector whose components are the limits of the component functions of r.

Find the lim r(t) as t approaches 0 where,

r(t) = (1+t³)i + (te⁻¹)j + (sint/t)k

r(t) = (1+t³)i + (te⁻¹)j + (sint/t)k

The corresponding parametric equations are,

x = 1 + t

y = 2 + 5t

z = ⁻1 + 6t

Note that this means that these are parametric equations of a line passing through the point

(1,2,⁻1) and parallel to the vector

<1,5,6> according to section 10.5

x = 1 + t

y = 2 + 5t

z = ⁻1 + 6t

Note that this means that these are parametric equations of a line passing through the point

(1,2,⁻1) and parallel to the vector

<1,5,6> according to section 10.5

Describe the curve defined by the vector function,

r(t) = <1+t,2+5t,⁻1+6t>

r(t) = <1+t,2+5t,⁻1+6t>

Sketch the curve whose vector equation is,

r(t) = (cost)i + (sint)j + (t)k

r(t) = (cost)i + (sint)j + (t)k

Use the line segment equation from 10.5

Find a vector equation and parametric equations for the line segment that joins the point,

P(1,3,⁻2)

to the point,

Q(2,⁻1,3)

P(1,3,⁻2)

to the point,

Q(2,⁻1,3)

Find a vector function that represents the curve of intersection of the cylinder,

x² + y² = 1

and the plane,

y + z = 2

x² + y² = 1

and the plane,

y + z = 2