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Rn

n = 2

3

(t)

R2

R3

(t)

(t) = (x(t), y(t))

(t) = (x(t), y(t), z(t))

I

II

x(t)

y(t)

z(t)

t

x y

z

t

t

t

(t)

t

t

(t)

(t)

x= x(t) y= y(t)

z= z(t)

t

t

: A R Rn n= 2 3 A

(t) = (x(t), y(t), z(t))

x(t)

y(t)

z(t)

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(A) ={(t) Rn | tA}

(t) = (2 +t, 1 +t2)

t[1, 4]

(t) = (2t + 1, 1 t)

(3, 0)(R) (2, 1) /(R)

(t) = (2 +t, 1 +t2)

t[1, 4]

(t) = (2t+ 1, 1 t)

(t) = (2+t, 1+t2)

t[1, 4]

(t) = (2t+ 1, 1 t)

(t) = (2 +t, 1 +t2)

t[1, 4]

(t) = (2t+ 1, 1 t)

(t) = (2 t, 2t+ 1, 3t)

(2, 1, 0)

(0, 3, 3)

(R)

(t) = (2 t, 2t+ 1, 3t)

(t) = (1 t)A + tB

([0, 1])

A= (0, 1) B = (1, 3) A= (1, 1) B = (1, 3) A= (1, 0, 2) B = (2, 2, 3)

(0) = (1,1)

(1) = (2, 3)

(t) = (2cos(t), 2sen(t))

t R

1

1(t) = (cos(t), sen(t)) 2(t) = (cos(2t), sen(2t))

3(t) = (cos(at+b), sen(at+b)), a= 0 4(t) = (sen(t), cos(t))

(t) = (44t, 2t) (t) = (2 +4t, 12t)

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(t) = (2 + cos(t), 1 + sen(t))

(t) = (t3, t2)

(t) = (t2, t)

(t) = (t2, t4)

(t) = (2+ cos(t), 1+sen(t))

(0)

(

6)

(4

) (

3)

(

2)

(t) = (t2, t)

(0)

(1)

(1)

(

2)

(2)

(t) = (t3, t2)

(0)

(1)

(1)

( 6

4)

( 64)

(t) = (t2, t4)

(0)

(1)

(

1)

(

2)

(2)

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(t) = (cos(t), 1, sen(t))

(t) = (cos(2t), t, sen(2t))

(t) = (1 + 3t, 1, 1 +t)

(t) = (3 + 3t,3t, 3 + 2t)

t= 0

(t) = (cos(t), 1, sen(t))

x 12

=y+ 1

3 =

z 12

x2 y2 = 1

1669

1690

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1696

XVII

1697

P

C

s

C x=|OT||PQ|

y=|CT| |CQ|

s

X

C (0, r)

P

P = (x, y)

C

OT

T P

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