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Mathematics
Mathematics
Problem
9. Find the angle between the following pair of lines: (i)
x
−
2
2
=
y
−
1
5
=
z
+
3
−
3
\frac{x-2}{2}=\frac{y-1}{5}=\frac{z+3}{-3}
2
x
−
2
=
5
y
−
1
=
−
3
z
+
3
and
x
+
2
−
1
=
y
−
4
8
=
z
−
5
4
\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}
−
1
x
+
2
=
8
y
−
4
=
4
z
−
5
(ii)
x
2
=
y
2
=
z
1
\frac{x}{2}=\frac{y}{2}=\frac{z}{1}
2
x
=
2
y
=
1
z
and
x
−
5
4
=
y
−
2
1
=
z
−
3
8
\frac{x-5}{4}=\frac{y-2}{1}=\frac{z-3}{8}
4
x
−
5
=
1
y
−
2
=
8
z
−
3
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