(−1,3,6),B(−6,2,6),C(−3,7,10).
1)
AB
=(−6+1,2−3,6−6)=(−5,−1,0)
=−5
i
−
j
,∣
∣=
25+1
=
26
AC
=(−3+1,7−3,10−6)=(−2,4,4)
=−2
+4
k
4+16+16
36
=6
\begin{gathered}2)\; \; \overline {AB}\cdot \overline {AC}=10-4+0=6cos\varphi =\frac{\overline {AB}\cdot \overline {AC}}{|\overline {AB}|\cdot |\overline {AC}|} =\frac{6}{\sqrt{26}\cdot 6}=\frac{1}{\sqrt{26}}varphi =arccos\frac{1}{\sqrt{26}}\end{gathered}
2)
⋅
=10−4+0=6
cosφ=
∣
∣⋅∣
⋅6
6
1
φ=arccos
\begin{gathered}3)\; \; A(x-x_0)+B(y-y_0)+C(z-z_0)=0-5\cdot (x+3)-1\cdot (y-7)+0\cdot (z-10)=0-5x-y-8=0pi :\; \; 5x+y+8=0\end{gathered}
3)A(x−x
0
)+B(y−y
)+C(z−z
)=0
−5⋅(x+3)−1⋅(y−7)+0⋅(z−10)=0
−5x−y−8=0
π:5x+y+8=0
ну вроде так
(−1,3,6),B(−6,2,6),C(−3,7,10).
1)
AB
=(−6+1,2−3,6−6)=(−5,−1,0)
AB
=−5
i
−
j
,∣
AB
∣=
25+1
=
26
AC
=(−3+1,7−3,10−6)=(−2,4,4)
AC
=−2
i
+4
j
+4
k
,∣
AC
∣=
4+16+16
=
36
=6
\begin{gathered}2)\; \; \overline {AB}\cdot \overline {AC}=10-4+0=6cos\varphi =\frac{\overline {AB}\cdot \overline {AC}}{|\overline {AB}|\cdot |\overline {AC}|} =\frac{6}{\sqrt{26}\cdot 6}=\frac{1}{\sqrt{26}}varphi =arccos\frac{1}{\sqrt{26}}\end{gathered}
2)
AB
⋅
AC
=10−4+0=6
cosφ=
∣
AB
∣⋅∣
AC
∣
AB
⋅
AC
=
26
⋅6
6
=
26
1
φ=arccos
26
1
\begin{gathered}3)\; \; A(x-x_0)+B(y-y_0)+C(z-z_0)=0-5\cdot (x+3)-1\cdot (y-7)+0\cdot (z-10)=0-5x-y-8=0pi :\; \; 5x+y+8=0\end{gathered}
3)A(x−x
0
)+B(y−y
0
)+C(z−z
0
)=0
−5⋅(x+3)−1⋅(y−7)+0⋅(z−10)=0
−5x−y−8=0
π:5x+y+8=0
ну вроде так
1) 5/7 = 5 ÷ 7 = 0,7142857143;
2) -8/15 = -8 ÷ 15 = -0,5333333333;
3) 8/9 = 8 ÷ 9 = 0,8888888889;
4) -2/21 = -2 ÷ 21 = -0,0952380952;
5) 5/22 = 5 ÷ 22 = 0,2272727273;
6) 4/45 = 4 ÷ 45 = 0,0888888889;
7) 1 4/11 = (1 × 11 + 4)/11 = 15/11 = 15 ÷ 11 = 1,3636363636;
8) 2 1/16 = (2 × 16 + 1)/16 = 33/16 = 33 ÷ 16 = 2,0625;
9) -1 2/3 = -(1 × 3 + 2)/3 = -5/3 = -5 ÷ 3 = -1,6666;
10) -1 1/27 = -(1 × 27 + 1)/27 = -28/27 = -28 ÷ 27 = -1,037037037;
11) 5 2/3 = (5 × 3 + 2)/3 = 17/3 = 17 ÷ 3 = 5,6666;
12) 4 5/6 = (4 × 6 + 5)/6 = 29/6 = 29 ÷ 6 = 4,8333333333;