fisica1-youn-e-freedman-exercicios-resolvidos

1.83: a) Parallelog ram area = 2 × area of triangle ABC
Triangle area = 1 2 base height = 1 2 B A sin θ
b)
o
90
Parellogram area = BA sin θ
( )( ) ( )( )
1.84: With the +x-axis to the right, +y-axis toward the top of the page, and +z-axis out
r r
r r
r r
2
2
A B = 87.8 cm , A × B = 68.9 cm , A × B = 0
×
x
y
z
of the page, ( ) ( ) ( ) .
1.85: a) A = ( 2.00) + ( 3.00) + ( 4.00) = 5.39.
b)
c)
B =
r r
A − B =
2
2
2
2
2
( 3.00) + ( 1.00) + ( 3.00) = 4.36.
=
( A − B ) iˆ
+ ( A − B ) ˆj
+ ( A − B )
x
x
( − 5.00) iˆ
+ ( 2.00) ˆj
+ ( 7.00)kˆ
2
2
2
( 5.00) + ( 2.00) + ( 7.00) = 8.83,
and this will be the magnitude of B
r − A
r
as well.
y
y
2
z
z
kˆ
1.86: The direction vectors each have magnitude 3 , and their dot product is (1) (1) +
(1) (–1) + (1) (–1) = –1, so from Eq. (1-18) the angle between the bonds is arccos
− 1
1 o
= arccos ( − ) = 109 .
= ( )
3
3
3