(−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
Пошаговое объяснение:
194.
1) 13:6 = 13/6 = 2 1/6
2) 43:5 = 43/5 = 8 3/5
3) 70:11 = 70/11 = 6 4/11
195.
1) 2 1/6 = 13/6
2) 1 12/17 = 29/17
3) 4 4/5 = 24/5
4) 12 7/20 = 247/20
196.
1) 9+3/17 = 9 3/17
2) 9/72+5 = 5 1/8
3) 4 5/18 + 2 4/18 = 6 9/18 = 6 1/2
4) 6 7/15 - 2 3/15 = 4 4/15
5) 9 11/16 + 4 3/16 - 2 2/16 = 13 14/16 - 2 2/16 = 11 12/16 = 11 3/4
6) 15 7/10 + 2 2/10 - 4 1/10 = 17 9/10 - 4 1/10 = 13 8/10 = 13 4/5
197.
1) 7 9/16 + 8 7/16 = 15 16/16 = 16
2) 4 9/19 + 5 13/19 = 9 22/19 = 10 3/19
3) 1 - 16/25 = 25/25 - 16/25 = 9/25
4) 4 - 1 7/12 = 3 12/12 - 1 7/12 = 2 5/12
5) 6 5/14 - 2 11/14 = 5 19/14 - 2 11/14 = 3 8/14 = 3 4/7
6) 19 11/35 - 12 29/35 = 18 46/35 - 12 29/35 = 6 17/35