Trabajo Colaborativo 1 Algebra Lineal

1. Dados los siguientes vectores dados en forma polar:

a. u = 5; q = 1350

b. v = 3; q = 600

Realice analíticamente, las operaciones siguientes:

1.1 2U ⃗+ V ⃗

1.2 V ⃗-U ⃗

1.3 (3V) ⃗-(4U) ⃗

Solución:

u ⃗ = (x , y) = ( |u| cos⁡θ, |u| sin⁡θ )

= (5 cos⁡〖135, 5 sin⁡135 〗)

= ( 5 (√2 )/(2 ) ,5 (√2 )/(2 )

= ( (-5√2)/2 , (5√2)/2 )

(v ) ⃗=( x ,y )=( |v| cos⁡〖θ ,|v|sin⁡〖θ )〗 〗

= (3 cos⁡〖60 , 3 sin⁡〖60 )〗 〗

= ( 3 1/2 ,3* 0.86 )

= ( 3/2 ,2.6 )

1.1 2u ⃗+ v ⃗=2 ((-5√2)/2 ,(5√2)/2 )+( 3/2 ,2.6 )

= ( -5√2 ,5√2)+( 3/2 ,2,6 )

= (3/2 -5√2 ,5√2+2,6 )

= ( -5,57 ,9.67 )

1.2 v ⃗- u ⃗=( 3/2 ,2,6 )-((-5√2 )/( 2 ) ,(5√2)/2 )

= ( 3/2 + (5√2)/2 ,2.6 (-5√2)/2

= (5.03 ,-0,93)

1.3 3v ⃗ - 4 u ⃗=3 ( 3/2 ,2,6 )- 4 ( (-5√2)/2 ,(5√2)/2 )

= ( 9/2 ,7,8 )- ( -10√2 ,10√2)

= ( 9/(2 ) +10√2 ,7,8-10√2)

= ( 18.64 ,-6.34)

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