Ecuaciones Parametricas

Ecuaciones paramétricas y simétricas

(1,-2,4) v=<2,4,-4>

X= 1+2t

Y= -2 +4t (x-1)/2=(y+2)/4=(z-4)/(-4)

Z= 4 -4t

(-2,1,0) (1,3,5)

V = <3,2,5> (x+2)/3=(y-1)/2=z/5

X= -2 +3t

Y= 1 +2t

Z= +5t

(0,0,0,) v=< 1,2,3 >

X= t x/1=y/2=z/3

Y= 2t

Z= 3t

( -3,5,4) (x-1)/3=(y+1)/(-2)=z-3

X= -3 +3t

Y= 5-2t (x+3)/3=(y-5)/(-2)=(z-4)/(-3)

Z= 4-3t

(-2,0,3) v=<2i,+4j -2k>

X= -2+2t

Y= +4t (x+2)/2=y/4=(z-3)/2

Z= 3-2t

(-3,0,2) v=<6j+3k>

X= -3

Y= +6t x+3=y/6=(z-2)/3

Z= 2+3t

(1,01,) X= 3+3t

Y= 5-2t

Z = -7+t

X= 1+3t

Y= 0-2t (x-1)/3=y/(-2)=(z-1)/1

Z = 1+t

(2,0,1) (1,4,-3)

V= < -1,4,-5>

X= 2- t (x-2)/(-1)=y/4=(z+5)/(-5)

Y= 0+4t

Z = 2-5t

(2,3,0) (10,8,12)

V= <8,5,12>

X= 2+10t (x-2)/10=(y-3)/8=z/12

Y= 3+8t

Z = 0+12t

(0,0,25) (10,10,0)

V=<10,10,-25>

X=0+10t

Y=0+10t x/10=y/10=(z-25)/(-25)

Z=25-25t

Ecuación del plano

Hallar la ecuación del plano que contiene a los puntos

(2,1,1), (0,4,1), (-2,1,4)

PQ V= <-2,3,0>

PR V=<-4,0,3>

I J K (X-2)9 + (Y-1)6 + (Z-1)12=0

-2 3 0 =9i+6J+12K 9X – 18 + 6Y – 6 + 12Z - 12=0

-4 0 3 9X + 6Y + 12Z = 36

(0,0,0) (1,2,3) (-2,3,3)

QR V= <-3,1,0>

QP V=< -1, -2, -3 >

I J K (X-1)(-3) + (Y-2)(-9) + (Z-3)7 =0

-3 1 0 = -3i - 9J + 7K -3X + 3 - 9Y + 18 + 7Z – 21 =0

-1 -2 -3 -3X - 9Y + 7Z = 0

(2,3,-2) (3,4,2) (1,-1,0)

QR V= <1,1,-4>

QP V=< -1, -4, -2 >

I J K (X-2)(-18) + (Y-3)(6) + (Z-(-2))(-3) =0

1 1 -4 = -18i + 6J - 3K -18X + 36 + 6Y - 18 - 3Z – 6 =0

-1 -4 -2 -18X + 6Y

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