02 vectores, parte 2
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Transcript of 02 vectores, parte 2
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)º180cos(2222 ABBAR
Si = 0º cos (180º) = 1 ABBAR 2222
222 2 BABAR 22 )( BAR
BAR
A B
R
A
BR
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)º180cos(2222 ABBAR
Si = 180º cos 0º = 1 ABBAR 2222
222 2 BABAR 22 )( BAR
BAR
A
BR
A
BR
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Las componentes de un vector son dos o más vectores que tienen
igual efecto que dicho vector.
Es decir, el vector dado es la resultante de las componentes.
Todo vector tiene un número infinito de conjuntos de componentes.
V
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Por componentes rectangulares u ortogonales nos referimos a
aquellas que están en ángulo recto una con la otra, y por lo general
se toman en las direcciones de las coordenadas rectangulares x y y.
x
y
V
Vx
Vy
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x
y
V
Vx
Vy
V
Vxcos
V
Vsen
y
cosVVx
VsenVy
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x
y
V
Vx
Vy
222
yx VVV
x
y
V
Vtan
22
yx VVV
x
y
V
V1tan
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x
y
A
A
B
BR
Ax
Ay
Bx
By
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x
y
R
Ax
Ay
Bx
By
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x
y
N
N
M
M
S
Mx
My
Nx
Ny
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x
y
S
Mx
My Nx
Ny
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x
y
45º
30º
4.5 u
5.0 u
9.0 u
3.2 u
3.2 u
7.8 u
4.5 u
4.6- 7.8 - 0 3.2 R x
3.7 4.5 - 5.0 3.2 R y
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x
y
4.6 u
3.7 u
22 )7.3()6.4(R
5.9 u
39º141º
6.4
7.3tan
4.6- 7.8 - 0 3.2 R x
3.7 4.5 - 5.0 3.2 R y
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Son vectores cuya magnitud es igual a la unidad.
x
y
i
j
A = 3i
A
B = 2jB
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x
yC = 3i 2j
CUc
Se puede determinar un vector
unitario en la dirección de
cualquier vector.
V
VUV
13C13
ˆ2ˆ3 jiUC
jiUCˆ
13
132ˆ13
133
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jiF
jiE
jiD
ˆ3ˆ2
ˆ2ˆ3
ˆ3ˆ2
FEDM
jijijiM ˆ3ˆ2ˆ2ˆ3ˆ3ˆ2
jiM ˆ2ˆ
FEDN 32
jiN ˆ15ˆ7
DFEP 32
jiP ˆ16ˆ10
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Utilizando seis palillos del mismo tamaño, sin romperlos, construir cuatro
triángulos equiláteros.
Un oso camina cien metros hacia el sur y luego cien metros hacia el este.
Finalmente camina cien metros hacia el norte llegando de esta manera al
punto de partida.
¿De qué color es el oso?
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x
y
z
V
abscisas
ordenadas
cotas
Vx
Vy
Vz
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x
y
z
V
Vx
Vy
Vz R
222
zx VVR
222
yVRV
222
zyx VVVV
V = Vx + Vy + Vz
V = Vxi + Vyj+ Vzk
ij
k
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x
y
z
V
Vx
Vy
Vz
V
Vxcos
V
Vycos
V
Vzcos
1coscoscos 222
cosenos directores