Post on 12-Jul-2016
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1. Encuentra la suma de los vectores u+v para cada inciso:
a) u = (5, -3) , v = (4, 2) b) u = (1, 7) , v = (2, -2)
ra = u + v = (5, -3) + (4, 2) = (9, -1) rb = u + v = (1, 7) + (2, -2) = (3, 5)
ra = (9, -1) rb = (3, 5)
Suma de los tres vectores
c) u = (-11, -6), v = (13, 9) R.= r1 + r2 + r3 = (9, -1) + (3, 5) + (2, 3) =(14,7)
r3 = u + v = (-11, -6) + (13, 9) = (2, 3) R = (14,7)
r3 = (2, 3)
2. Encuentra la magnitud del vector resultante de la suma de los vectores anteriores.
ra = (9, -1) | | √ √ rb = (3, 5) | | √ √
| | √ = 9.0553 | | √ = 5.8309
rc = (2, 3) | | √ √ Magnitud de la resultante R
| | √ = 3.6055 R = (14, 7) | | √ √
R = √ = 15.6524
ACTIVIDAD 2. “EJERCICIOS CON VECTORES”
3. Representa la suma de vectores en el plano cartesiano.
a) u= (B) = (5, -3) , v=(C) = (4, 2) b) u= (B) = (1, 7) , v=(C) = (2, -2)
ra = u + v = (5, -3) + (4, 2) = (9, -1) rb = u + v = (1, 7) + (2, -2) = (3, 5)
(b) = ra = (9, -1) = 9i - j = (B´) (b) = rb = (3, 5) = 3i + 5j = (B´)
(9, -1)
(3, 5)
𝒂𝒏𝒈𝒖𝒍𝒐 𝐜𝐨𝐬−𝟏 𝟏𝟒
√𝟑𝟒 ∗ 𝟐√𝟓 𝟓𝟕.𝟓𝟐°
Componentes
Vector unitario =ra = ( 𝟗
√𝟖𝟐 ,
𝟏
√𝟖𝟐 )
Angulo entre Vectores
𝒂𝒏𝒈𝒖𝒍𝒐 𝐜𝐨𝐬−𝟏 𝟏𝟐
𝟓√𝟐 ∗ 𝟐√𝟐 𝟏𝟐𝟔.𝟖𝟔°
Componentes
Vector unitario =rb = ( 𝟑
√𝟑𝟒 ,
𝟓
√𝟑𝟒 )
Angulo entre Vectores
3. Representa la suma de vectores en el plano cartesiano.
Suma de los tres vectores
c) u = (-11, -6), v = (13, 9) R.= ra + rb + rc = (9, -1) + (3, 5) + (2, 3) =(14,7)
rc = u + v = (-11, -6) + (13, 9) = (2, 3) ( f ) = R = (14,7) = 14i + 7j =(B´)
( b ) = rc = (2, 3) = 2i + 3j = (B´)
(2, 3)
(14, 7)
𝒂𝒏𝒈𝒖𝒍𝒐 𝐜𝐨𝐬−𝟏 𝟏𝟗𝟕
√𝟏𝟓𝟕 ∗ 𝟓√𝟏𝟎 𝟔.𝟎𝟖°
Componentes
Vector unitario =rc = ( 𝟐
√𝟏𝟑 ,
𝟑
√𝟏𝟑 )
Angulo entre Vectores
𝒂𝒏𝒈𝒖𝒍𝒐 𝐜𝐨𝐬−𝟏 𝟑𝟗
√𝟖𝟒 ∗ √𝟑𝟒 ∗ √𝟏𝟑 𝟕𝟖.𝟑𝟐°
Componentes
Vector unitario =R = ( 𝟏𝟒
𝟕√𝟓 ,
𝟕
𝟕√𝟓 )
Angulo entre Vectores
4. Encuentra la resta de los siguientes vectores. Y represéntalos en el plano.
1. u = (1, 1, 2) , v = (0, 2, 1)
r1 = u - v = (1, 1, 2) - (0, 2, 1) = (1, -1, 1)
b= r1 = (1, -1, 1) = i – j + k =(B´)
𝜶 𝒂𝒏𝒈𝒖𝒍𝒐 𝒅𝒆 𝒊 𝐜𝐨𝐬−𝟏𝟏
√𝟑 𝟓𝟒.𝟕𝟑°
𝜷 𝒂𝒏𝒈𝒖𝒍𝒐 𝒅𝒆 𝒋 𝐜𝐨𝐬−𝟏 𝟏
√𝟑 𝟏𝟐𝟓.𝟐𝟔°
𝜸 𝒂𝒏𝒈𝒖𝒍𝒐 𝒅𝒆 𝒌 𝐜𝐨𝐬−𝟏𝟏
√𝟑 𝟓𝟒.𝟕𝟑°
Componentes
Vector unitario =r1 = ( 𝟏
√𝟑 ,
𝟏
√𝟑,
𝟏
√𝟑 )
Magnitud del vector |r1|= √𝟑
Cosenos directores del vector r1
2. u = (6, 0, 2) , v = (3, 5, 1)
r2 = u - v = (6, 0, 2) - (3, 5, 1) = (3, -5, 1)
b = r2 = (3, -5, 1) = i – 5j + k = (B´)
|
𝜶 𝒂𝒏𝒈𝒖𝒍𝒐 𝒅𝒆 𝒊 𝐜𝐨𝐬−𝟏𝟑
√𝟑𝟓 𝟓𝟗.𝟓𝟐°
𝜷 𝒂𝒏𝒈𝒖𝒍𝒐 𝒅𝒆 𝒋 𝐜𝐨𝐬−𝟏 𝟓
√𝟑𝟓 𝟏𝟒𝟕.𝟔𝟖°
𝜸 𝒂𝒏𝒈𝒖𝒍𝒐 𝒅𝒆 𝒌 𝐜𝐨𝐬−𝟏𝟏
√𝟑𝟓 𝟖𝟎.𝟐𝟔°
Componentes
Vector unitario =r2 = ( 𝟑
√𝟑𝟓 ,
𝟓
√𝟑𝟓,
𝟏
√𝟑𝟓 )
Magnitud del vector |r2|= √𝟑𝟓
Cosenos directores del vector r1