Tarea 1 : Producto vectorial

PRODUCTO VECTORIAL

1. Si μ = (2,-1,3)

V = (0,1,7)

W = (1,4,5)

a) μX (VXW)

i j k

0 1 7 = (5-28)i – (0-7)j + (0-1)k = -23i +7j -1k

1 4 5

i j k

2 -1 3 = (1-21)i – (-2+69)j + (14-23)k = -20i -67j -9k

-23 7 -1

b) (μXV)XW

i j k

2 -1 3 = ( -7-3)i – (14-0)j + (2-0)k = -10i -14j +2k

0 1 7

i j k

-10 -14 2 = (-70-8)i – (-50-2)j +( -40+14)k = -78i +52j -26k

1 4 5

c) (μXV)- 2W

i j k

2 -1 3 = ( -7-3)i – (14-0)j + (2-0)k = -10i -14j +2k

0 1 7

(μXV)- 2W = -10i -14j +2k – 2(1, 4, 5)

= -10i -14j +2k – 2i – 8j – 10k

= -12i - 22j - 8k

2. Hallar el área del triangulo que tiene vértices P,Q,R.

P( 1,5,-2)

Q( 0,0,0)

R ( 3,5,1)

P₁P₂ (-1,-5,2)

P₁P₃ (2, 0, 3)

P₁P₂ X P₁P_{3 =} i j k

-1 -5 2 = ( -15-0)i – (-3-4)j + ( 0+10)k

2 0 3

= -15i +7j +10k

= √(-15i) +(7j) +(10k)

= 19.33 / 2

= 9.66