Tarea de Repaso

Repaso:

1) Si:

µ = (2, -1, 3)
v = (0, 1, 7)
w = (1, 4, 5)

a) µ x (v x w)

i-----j---k
0---1---7 = [(1 x 5)–(4 x 7)]î - [(0 x 5)–(1 x 7)]ĵ + [(0 x 4)–(1 x 1)]k̂
1---4---5 -----------------------------= -23i + 7j – 1k


---i----j---k
---2---1---3 = [(-1 x -1)–(7 x 3)]î - [(2 x -1)–(-23 x 3)]ĵ + [(2 x 7) – (-23 x -1)]k̂
-23---7---1----------------------- = 20i – 67j – 9k =-56


b) (µ x v) x w

i---- j---k
2 --1---3 = [(-1 x 7) – (1 x 3)]î - [(2 x 7) – (0 x 3)]ĵ + [(2 x 1) – (0 x -1)]k
0---1---7----------------------------= -10i – 14j + 2k

---i-----j-----k
-10--14----2 = [(-14 x 5) – (4 x 2)]î - [(-10 x 5) – (1 x 2)]ĵ + [(-10 x 4) – (1 x -14)]k
---1----4----5----------------------= -78i + 52j -26k = -12

c) (µ x v) -2 w

-2 (1, 4, 5) = -2, -8, -10
(-10, -14, ) + (-2, -8, -10) = -12 -22 -8

2) Hallar el área del triangulo que tiene vértices P, Q, R
P (1, 5, -2)
Q ( 0, 0, 0)------------------------(-1, -5, 2) (2, 0, 3)
R (3, 5, 1)

------------→ ---------→------------2
A = ½ //P₁P₂ x P₁P₃// = ______ = 9.66
--------------------------------------19.33

--→---------→--------i-----j----k
P₁P₂ x P₁P₃ = -1-----5---2 = [(-5 x 3) – (0 x 2)]î - [(-1 x 3) – (2 x 2)]ĵ
--------------------------2-----0---3--------------------+ [(-1 x 0) – (2 x -5)]k̂
------------------------------------------------------------= -15i + 7j + 10k