HEEEEEEEEEEEEEEEEEEEEELP. Created by Katia1981. matematika-ru

HEEEEEEEEEEEEEEEEEEEEELP...

Katia1981 @Katia1981

July 2022 1 5 Report

HEEEEEEEEEEEEEEEEEEEEELP

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sharadi

Verified answer

№1 → x y z → x y z
а) а {5; -3; 7}, b {2;11;-2}, α = π/6
→ → → → →
[a * b] = (-3*(-2) - 7*11) i + (7*2 - 5*(-2)) j +(5*11 - (-3)*2) k=
  → → →
=-71 i + 24 j +49 k
  → →
| [a * b] | = |a| *|b|*Sinα= √(25+9+49) *√(4 +121+4) * 1/2 = √93*√129*1/2=
= 1,5√1333
→ →
в)|[a * b]| = √(1 +2 +9)*√(9 +16 + 25) * √3/2 = √12*√50*√3/2 = 15√2
→ →
с) |[a * b]| = √(1 +16 +36)*√(25 +25 +1) * 1= √53*√51 = √2703
№2
А(1;2;3), В(4;-1;3); С(3; -5; 3); D(2; 6; -1); Е(4;10;5); R(4;-1;-1)
→ → →   →   →
АС{2; -7;0} , BD{-2;7;-4}, DC{1;-11;4}, RC{-1;-4;4}, ED{-2;-4;-6},
→
DR{2;-7;0},
→    →   → → →
[AC * BD] = ((-7)*(-4) -0*7) i + (0*(-2)-2*(-4)) j +(2*7 - (-7)*(-2)) k =
→ → →
=28 i +8 j +0k
→   → → → →
[DC* RC] = ((-11)*4 - 4*(-4))i +(4*(-1) - 1*4)j + (1*(-4)-(-11)*(-1))k=
→ → →
=-28 i -8j -15k.
→   →   → → →
[ED*DR] = ((-4)*0 - (-6)*(-7))i + ((-2)*2 - (-2)*0) j + ((-2)*(-7) -(-2)*2) k =
  → →   →
= -4 2i -4j +10k.
№3
→ →   →
i {1; 0; 0;}, j {0;1;0} , k{ 0;0;1}
→ →   → → →   →   → → → →
i - k{1;0;-1}, i + j + k{1;1;1}, ( i  -  k)*( i + j + k) = 1 + 0 -1 = 0
  → →   → → →
|[(i - k)*( i + j + k)] | = 0

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