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,..01 12. M0(-2; -2; 3), M1(4; 6; 2), M2(-6; 12; 3), M3(-2; 0; 1). а) M1(4; 6; 2), M2(-6; 12; 3).
x1 = 4; y1 = 6; z1 = 2; x2 = -6; y2 = 12; z2 = 3
x − x1 x2 − x1
x − x2 |
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x2 − x1 |
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x − 4 |
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−10 |
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x + 6 |
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−10 |
б)
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y − y1 |
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y2 − y1 |
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y − y2 |
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y2 − y1 |
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y − 6 |
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6 |
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y − 12 |
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6 |
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z − z1 |
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z2 − z1 |
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z − z2 |
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z2 − z1 |
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z − 2 |
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z − 3 1
M1M30 = (x3 − x1)(y3 − y1)(z3 − z1)
M1M |
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= (x − x1)(y − y1)(z − z1) |
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M1M2 |
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= (x2 − x1)(y2 − y1)(z2 − z1) |
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x2 − x1 = −10 |
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x3 − x1 = −6 |
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y2 − y1 = 6 |
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y3 − y1 = −6 |
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z2 − z1 = 1 |
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z3 − z1 = −1 |
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x − 4 |
y − 6 |
z − 2 |
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−10 |
6 |
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−6 |
−6 |
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x − x1 = |
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x − 4 |
y − y1 = |
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y − 6 |
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z − z1 = |
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z − 2 |
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(x − 4) |
6 |
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− (y − 6) |
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−10 1 |
+ (z − 2) |
−10 |
6 |
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−6 |
−1 |
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−6 −1 |
−6 |
−6 |
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(x − 4)(6 −1 − −6 1) − (y |
− 6)(−10 −1 |
− −6 1) + (z − 2)(−10 −6 − −6 6) = |
−16y + 96z − 96 |
г)
![](/html/92241/572/html_5MeuHoVhUR.CcHd/htmlconvd-ZX4aF62x1.jpg)
в) Для вычисления расстояния от точки M(Mx; My; Mz) до плоскости Ax + By + Cz + D = 0
используем формулу:d = |A·Mx + B·My + C·Mz + D|√ A2 + B2 + C2
Подставим в формулу данные:
d = |0·(-2) + (-16)·(-2) + 96·3 + (-96)|√ 02 + (-16)2 + 962 = |0 + 32 + 288 - 96|√ 0 + 256 + 9216 =
= 224√ 9472 = 14√ 37 37 ≈ 2.301585822275002
![](/html/92241/572/html_5MeuHoVhUR.CcHd/htmlconvd-ZX4aF63x1.jpg)