Vector Methods
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7/31/2019 Vector Methods
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AC = AB + BC
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a + b = b + a
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AB + BC = AC
AB + BC + CA = AC + CA
AB + BC + CA = 0
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nth
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( a + b ) + c = a + ( b + c )
a b = a + ( b )
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OB = OA + AB = P + Q
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AC = AB cos = Q cos
BC = AB sin = Q sin
OB =
OC2 + BC2
= { ( OA + AC ) 2 + BC2 }
OB =
( P + Q cos )2
+ Q sin 2
OB =
P
2 + Q2 cos 2 + 2PQ cos + Q2 sin 2 R = O B = P2 + 2PQ cos +
Q2
tan = BCOC =Q sin
P + Q cos
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OB = P2 + Q2
tan = QP
R =
r2 + r2
=
2r
R = O B + R = r +
2r = ( 1 +
2 ) r
3a2
+ b2
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R = { ( a + b ) 2 + ( a b ) 2 + 2 ( a + b ) ( a b ) cos }
3a
2 + b2 =
{( a + b )
2+ ( a
b )
2+ 2 ( a + b ) ( a
b ) cos
}
3a2 + b2 = { ( a + b ) 2 + ( a b ) 2 + 2 ( a + b ) ( a b ) cos
}
cos = ( a2 b2 )
2 ( a2 b2 ) =12 = cos60
= 60
| a + b | | a | + | b |
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OC < OA + AC
OC < OA + OB
| a + b | < | a | + | b |
OC = OA + OB
| a + b | = | a | + | b |
| a + b | | a | + | b |
| a b | | a | | b |
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ABsinBCA =
BCsinCAB =
CAsinABC
AB
sin ( ) =
BC
sin ( ) =
CA
sin ( )
ABsin = BCsin = CAsin
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R = 10 + 25 = 35 N
R = 25 10 = 15 N
5 + 9 < 17
