calculo vectorial

Taller evaluativo de cálculo vectorial

Elaborado por: Brigite Johana Daniels Sarabia, angélica Gómez Hernández
Grupo :GD

1) P ( 3 , 1 ,2) N = < 1,2, -3 >

a). ( ) + b ( ) + c ()

( x – 3 ) + 2 ( y -1 ) – 3 ( z – 2 ) = 0

X – 3 + 2y – 2 – 3z + 6 = 0

X + 2y – 3z + 1 = 0


2) P (-3 , 2 , 5) N = < 6, -3, -2 >

a). ( ) + b ( ) + c ( )

6 (x + 3) – 3 ( y– 2) – 2 ( z – 5) = 0

6x + 18 – 3y + 6 – 2z + 10 = 0

6x – 3y – 2z + 22 = 0


3) A. ( 3, 4, 1) B ( 1, 7 , 1) C ( -1, -2, 5)

ax + by + cz + d = 0

< - 2, 3, 0 > < - 2, -9, 4 >< - 2, 3, 0 > < - 2, -9, 4 >


= (12 – 0) i - (-8 – 0) j + (18+6) k

= 12 i + 8 j + 24 k → ÷ 4
3 x + 2 y + 6 z = 23

4) A. ( 0, 0, 2) B ( 2, 4 , 1) C ( -2, 3, 3)

ax + by+ cz + d = 0

< 0 , 0 , -1 > < - 4, -1, 2 >

< 0 , 0 , -1 > < - 4, -1, 2 >


= (0 + 2) i - (0 + 5) j + (0 - 0) k = 2 i – 5 j


5) P ( 2 , 6 , -1 )

Ecuación → 4 x –2 y + z – 1 = 0

< a , b , c > . < 4 , -2 , -1 > = 0

4 a - 2 b - c = 0

a x + b y + cz = 0

4 a (x-2) + 2b (y – 6) + c (z + 1) = 0

4x – 8 + 2y – 12 + z + 1 = 0

4 x + 2y + z - 19 = 0


6)

1) 2x – y – 2z – 5 = 0

2) 6x – 2y + 3z + 8 = 0


N1 = 2i – j – 2k N2 = 6i – 2j + 3k








= = 0,38

Θ = ( 0,38 ) = 67°








8) P (2,2,-4)2 2 -7

Ecuación → 2x + 2y – z – 6 = 0

d =

d = = d = d = d =

13) 10 , 5 , 21

P (-2,2,2) ; Q (-8,1,6) ; R (3,4,-1)

< 11 , 3 , -7 > < 5 , 2 , -3 >

= (- 9 + 14) i – (-33 + 35 ) j + ( 22 – 15 ) k

= 5 i – 2 j + 7 k

5 x – 2y + 7z = 0


14) P ( 2 , 3, 0 ) Q ( 2, 0 , 4 ) R ( 0 , 3 , 4 )

< -2 , 0 , 4 > < -2 , -3 , 0 >

= (0+12) i – (0+8) j + (6-0) k= 12 i – 8 j + 6 k

12 x – 8y + 6z = 0

10) Puntos.






= Q – P = ( 1, 1, 3) (-2, 1, -1)
= < 3 , 0 , 4 >

= P – S = ( -8, 4, -4) (-2, 1, -1)
= < -6 , 3 , -3 >

= R...