Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 51 стр.

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D(v)
v Φ
u ∈ V
n−1
(D(v))
{u
j
} a
ij
v
i
x
j
= 0
M
0
(x
i
0
)
Φ ` x
i
= x
i
0
+ v
i
t
M
0
M
0
(x
i
0
) ∈ Φ F (x
i
0
) = 0
ϕ(v)t
2
+ F
i
(x
k
0
)v
i
t = 0.
M
0
(x
i
0
) ` Φ
t
1
= t
2
= 0
M
0
`
Φ
F
i
(x
k
0
)v
i
= 0 (a
ij
x
j
0
+ a
i n+1
)v
i
= 0.
M
0
Φ
∇F (M
0
) {F
1
(x
k
0
), . . . , F
n
(x
k
0
)}
∇F (M
0
)
A
n
F
i
0
(x
k
0
0
) = p
i
i
0
F
i
(x
k
0
)
M
0
T
M
0
Φ
v (60)
n−1 V
n
Φ M
0
π
M
0
(Φ) M
0
Φ T
M
0
Φ
Φ M
0
π
M
0
(Φ)
F
i
(x
k
0
)(x
i
− x
i
0
) = 0
(a
ij
x
j
0
+ a
i n+1
)(x
i
− x
i
0
) = 0.
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