Álgebra Lineal

1. vectores dados en forma polar

a.‖u‖=5;θ=225°

U_X=5*cosθ225° U_y=5*senθ225°

U_X=5*(√2/2) U_y=5*(√2/2)

U_X=(5√2)/2 U_y=(5√2)/2

((-5√2)/2, (- 5√2)/2 )

ghh

b.‖v‖=3;θ=60°

v_X=3*cosθ60° v_y=3*senθ60°

v_X=3*(1/2) v_y=3*(√3/2)

v_X=3/2 v_y=(3√3)/2

(3/2, (3√3)/2 )

1.1.

2((-5√2)/2, (- 5√2)/2 )-6(3/2, (3√3)/2 )

(-5√2 ,-5√2 ) + (-9-9√3 )

(-5√2-9 ,-5√2 -9√3)

,(-16.1,-22.7)

R √((-16.1)^2+(-22.7)^(2 ) )=27.8

Tanθ R_Y/R_X =(-22.7)/(-16.1)

θ=〖Tan〗^(-1) (-22.7)/(-16.1)=54.6°

180°+54.6°=234,6°

r =27.8 θ=234,6°

1.2. □(→┬(v )- □(→┬u ))

((-5√2)/2, (- 5√2)/2 )-(3/2, (3√3)/2 )

((5√2+3)/2) (4√2)

(5,5.6)

√((5)^2+(5.6)^(2 ) )

√(25+31.36 )

√56.36

=7.5

Tanθ R_Y/R_X =5/5.6

θ=47°

1.3

6(3/2, (3√3)/2 )-7((-5√2)/2, (- 5√2)/2 )

(35√2)/2, (3 5√2)/2 + (-9-9√3 )

( (35√2)/2-9, (35√2)/2-9√3)

(15.7,9.1)

R √((15.7)^2+(9.1)^(2 ) )=18.14

Tanθ R_Y/R_X =9.1/15.7

θ=〖Tan〗^(-1) 9.1/15.7=30°

θ=30°

2.1 (u ) ⃗=2i ̂+9j ̂ y v ⃗-6 i ̂+9j ̂

csc⁡∝=((2 .6)+(9 .9))/(√(〖(2)〗^2+〖(9)〗^2

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