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Mathematics
Mathematics
Problem
Let the equation of the plane containing the line of intersection of the planes
x
−
y
−
z
−
4
=
0
x - y - z - 4 = 0
x
−
y
−
z
−
4
=
0
and
x
+
y
+
2
z
−
4
=
0
x + y + 2z - 4 = 0
x
+
y
+
2
z
−
4
=
0
, and parallel to the line of intersection of the planes
2
x
+
3
y
+
z
=
1
2x + 3y + z = 1
2
x
+
3
y
+
z
=
1
and
x
+
3
y
+
2
z
=
2
x + 3y + 2z = 2
x
+
3
y
+
2
z
=
2
, be
x
+
A
y
+
B
z
+
C
=
0
x + Ay + Bz + C = 0
x
+
A
y
+
B
z
+
C
=
0
. Then the value of
∣
A
+
B
+
C
−
4
∣
|A + B + C - 4|
∣
A
+
B
+
C
−
4∣
is .....
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