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Mathematics
Mathematics
Problem
Statement I
The lines
x
−
1
1
=
y
−
1
=
z
+
1
1
\frac{x-1}{1} = \frac{y}{-1} = \frac{z+1}{1}
1
x
−
1
=
−
1
y
=
1
z
+
1
and
x
−
2
1
=
y
+
1
2
=
z
3
\frac{x-2}{1} = \frac{y+1}{2} = \frac{z}{3}
1
x
−
2
=
2
y
+
1
=
3
z
are coplanar and equation of the plane containing them is
5
x
+
2
y
−
3
z
−
8
=
0
5x + 2y - 3z - 8 = 0
5
x
+
2
y
−
3
z
−
8
=
0
Statement II
The line
x
−
2
1
=
y
+
1
2
=
z
3
\frac{x-2}{1} = \frac{y+1}{2} = \frac{z}{3}
1
x
−
2
=
2
y
+
1
=
3
z
is perpendicular to the plane
3
x
+
6
y
+
9
z
−
8
=
0
3x + 6y + 9z - 8 = 0
3
x
+
6
y
+
9
z
−
8
=
0
and parallel to the plane
x
+
y
−
z
=
0
x + y - z = 0
x
+
y
−
z
=
0
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