ACTIVIDAD DE ALGEBRA - VECTORES

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33. calcule u + v

U + v = (2+2,3+3,4+5) = (4i, 6j, 9k)

35. calcule 3u – 2v

U= 3(2,-3-4) = (6, -9,12)

V= 2(-2,-3,5) = (-4,-6-10)

3u-2v= (6 – (-4), -9 – (-6), 12-10) = (10, -3, 2) [pic 81]

37, calcule 2u + 7w + 5v

2u= 2(2,-3,4) = 4,-6,8)

7w = 7(1,-7,3) = (7,-49,21)

5v = 5(-2,-3-5) = (-10,-15,25)

= 2u+7w+5v= (4+7 + (-10), -6 + (-49) + (-15), 8+21+25) = (1, -70. 54)

39. calcule 2v + 7t – w

2v= 2(-2,-3,5) = (-4,-6,10)

7t= 7(3, 4,5,) = (21, 28,35)

= 2v+7t-w = (-4+21-1, -6+28-(-7), 10+35-3) = (16, 29,42)

41. calcule (3t-2u)*(5v+2w)

3t= 3(3, 4,5,) = (9, 12,15)

2u= 2(4,-6,8)

5v= 5(-10,-15,25)

2w= 2(1,-7,3) = (2,-14,6)

=3t-2u= (9-4, 12-(-6), 15-8) = (5, 18,7)

= 5v+2w= (-10+1, -15 + (-7), 25+3) = (-9,-22,28)

(3t-2u)*(5v+2w)= (5, 18,7)*(-9,-22,28) = (5.-9, 18.-22, 7.28,) = (-45, -396, 196)

43. calcule u*w – w*t[pic 82]

U*w= (2.1, -3.-7, 4.3) = (2, 21, 12)

W*t = (1.3, -7.-4, 3.5) = (3, -28-15)

= u*w-w*t= (2-3, 21 – (-28), 12, 15) = (-1, 49,-3)

45. calcule el ángulo entre t y w

[pic 83]

[pic 84]

[pic 85]

[pic 86]

47. calcule proy^t w

[pic 87]

= (3, 4,5,) .(1,-7,3) = 3+28+15= -10

= (3,4,5) .(3,4,5) = 9+16+25 = 50

[pic 88]

[pic 89]

Página 261[pic 90]

En los problemas 1 al 26 encuentre el producto cruz u x v.

1. u = i – 2j v = 3k

[pic 91]

Uxv = [-6-1] i – [3-1]j + [1+2]k

Uxv = -7i+2j+3k = (-7, 2, 3)

3. U = 2i – 3j v = -9i +6j

[pic 92]

Uxv = -18i + -7j = (18, 7)

5. U = -7k v= j + 2k

[pic 93]

Uxv= -14j-1k = (-14, 1)

7. u = -2i + 3j v= 7i+ 4k

[pic 94]

Uxv= [12-1]I – [-8-7]j + [-2-21] k

Uxv= 11i-15j + 23k = (11,-15, 23) [pic 95]

11. u= 2i-3j+k v= i+2j+k

[pic 96]

Uxv = [-3-2] i – [2-1] j + [4- (-3)] k

Uxv= 5i+1j+7k = (5, 1, 7)

13. U= I + 2j + k v= -I +6j-k

[pic 97]

Uxv= [-2-6]I – [-1-(-1)] j + [6-(-2)] k

Uxv= 8i+0j+8k = (8, 0, 8)

15. u= I + 7j – 3k v= -I -7j +3k

[pic 98]

Uxv = [21-21] I – [3-3] j + [-7-(-7)] k

Uxv= (0, 0, 0)

17. U= 2i – 3j + 5k v= 3i –j –k

[pic 100][pic 99]

Uxv = [3-(-5)] I – [-2-15] j +[-2 –(-9)] k

Uxv= 8i- 17j + 7k = (8,-17, 7)

19. u = 10 I + 7j – 3k v= -3i + 4j -3k

[pic 101]

Uxv = [-21 – (-12)] I – [-30-9] j + [40- (-21)] k

Uxv= -9i-39j + 6k = (-9,-39, 6)

21. u= -i -2j + 5k v= -2i +4j + 8k

[pic 102]

Uxv= [-16-20] I – [-8-(-10)] j + [ -4-4] k

Uxv= 36i +2j -8k = (36, 2,-8)

23. u = 3i – j + 8k v= I + j -4k

[pic 103]

Uxv = [4-8] I – [ -12-8] j + [3 – (-1)] k

Uxv= -4i -20j + 4k = (-4,-20,4)

[pic 104]